Bangladesh Physics Olympiad

Sample Problems

Forrnrjc SbteeL fop Gt4aPY B

A ssu^g trtr c-obruafuorc

s= uLL $aV2= +0s

n jnitia sp^LV = ftaf ptlg = 6Ihhwa enuA

Nartong eod Laco i r - lrr

f =rna or7= or F ^u -

1l- ampfJrrtaL e1u-aEot+t vttur -lta- xilvel- + d er x-

lr4r^L[enr-- 4hdL -lt u4 tn4-A tlHilf fiL frot-

is rypfrnfo^ oi + oT v

Iie^rbnl 2A Le iw -b-

TIw do|= 6 Yx+ -Jtuz W ennArnzd ito

wo -fto WJhf -effA^ilrtrt wQ- -

f= nft- n=^^A F6= ^oy

F Ab = P ^ trarnrio fu-dip-

e) rrp- + q^rhfl-kff T ffi bd

b ffrnw-droru -fuEfi^

amp= ryf6ravito[t onaL pd^tiot tt] if ^ ^ 0r a- P6Rt Tl

otho|q- tt^r- Qgnt6g racltue ampr o -

6F8 = -6 El+k-=-icry

frah^v frr drw poulbrv p a puwholo- Lndep cL ra$b^ri tucl

Mea is(= Astdf f e)

-i1 = Awoo+S)

alurutirj ffiT

IF dr4+iuiaL qoh= SY ct

g)= anr6rw vryy = T0^t- ptIAilwt ts

ffi71 +-y-

ltr ffin nnlrU c4^atior ftr cL- Vnau0-$-t$ s6ruhrrt ts

n^n^fr JUgdYfi 6rffitrltrTnamprivc- wu- Silttt elurtrru th^b cgvLhe dpa t^r

cors^fur pt- tut 01^ fr )ttttr o^d- fraF u^oq]

-- F= n^i or --t =Jx

1e -= CDI At-f

drn = al A

zlT

= O

+ T znrftrt-uf-

T= tnrF 1

i+=0coz= L

yn

Kr= rnulContof wlur^ ggf A 6^r

fr^vi+3h =wr$tth

E

t(s-F

P= 4E_db

Kr+ RE C

A

h1v2-

hL

r vut^

r=j-

fr te a satrbvra-nr u tyro- ^drtq$hit Ia-- ts G+$icampl[a-

Flfn pF)= rto) -uf1- -- I Bftz) o-^ urott-n-^ssrin il^ph turif a-t cl

l_lt- ^^ ea-t t cswMvb rrtqnar ff- $^i1t-+ poJ

rfpJ bryat cw +-

pa- pqSrzesvc travoa

d = cto^(t-kq h= +-a

ft= fuspfarurrulb afr aL rrlfuaiL aL ayive-^ poinF i^j ( lndin^

co an5wr ftryt^g of ostltrd^-atuJ oJ fu- prutuclr

(x= dx^rc-- eow ^W fi^uu-uvz- ala^4- lfu x--direthcrn

wampva- wlodtS (u)fZ = fix T= fr = ^tinbt-ktfi = aar crs(3t -kDd

Y - Nasi nt-kf

vrtqxi rlr^nv banttctJl ^eLoci f1 = acc

YvraXirrrrurn pnrrhUr- arc-erdarticr = 4c2

ThB pryakort- relfris lrt ^rnptbn o$ a pcudL irtHrvffvJlxnN-

tD frb cnoh0ru ctf rc- vra-v a

hruot at oxPwtaiun -l

Pl

il_xg

t= b

ts

5e--A ftrw hhD$L evtuvsian

Aa= A(1 ops) f =

hfu-tfrcrrnaL exPaAsiolu I

Vs= U(1+Ye)

ES-

5VY=-v

amps

p=zd -=3d

O fu$swJ

= W ufty yq P$u L^vU ba-

k = -WwrnaL csndunnZ

TWO1 a^d

QD q =rn[-

E=rnctT

f rV)rw qV c a^lfir

i = r

(9Alrr- ^-r fiunL tu--ry ^A ltdirn f er^f-lj^ (- Y

t-J

6tA r J- =- r__ s5r g

Siw uwveninns i

-

fD iS pesitra for ^ cnncLveuro rnirrrof a^LI

ywLt ( o rs is pasibve

v-rrahra]- iofr

ou CffrVOc

a-T

gpepnaL conJuAtm)

k A fg- )7c

=-s F vnalirraS q cnvLaVB Jens] I

urpe- X = disfurr1ap-- rl]rk-cb ampn Sq-nvtC n rtr f

$namp -fi^L obrqf [s re-aL tA naCr-ve

uI

Lg-nSr

l-r I5SDYa

Ngt( -

s infucqlas

fn au hine )ans

t =G 9tt +)frgt= relrmte- uAr o le-os

h r = reurod6+ femampe- LAzx eurotr-frou^e nL

( and A es(w rdn 4 f sa|a qf fl^ JjrJ

RaEutrr^-- -=---- o

^ =_ sln I

5i^ t

rf = L-- uiJL(eL i aeuoaampffirr-

Fk^ficilv c_ __v - _ - a o

$= IR [ovit

fu amp=

[]

t P-xrut]

a s rnaJl urerf rrrrt -

feoU- Sava-tV

P= f V =TR

lA^ i dL x ftv _-4x hz

I)o i Llsin94F YL

hZRr+

ng_t(- Rtl

Laflrrfik- r amp^a- bdu

6n lrl Blr raLw

t4aqrpI^D |4terAr- t^ )w2 etutevtt- -tiltYi9 d9 qL a- l

Adbaha-e- n 4rrrn $r- ^Hc t

z[r

)iuLL oh U^ eu$t- o-- ^ s6b-niAuB

= ry Tf=lra -rturilnh- r+ ry^vL

B=ampt

[aprah-L

naBe4

r^rtrunk

f = --lrf$ ftavA^1a W^r of dtrtnoTamp i-fu

futes- ouv) a- errrant Cgrr$ih t^ri-leuro- rn an ehnA b dzlA

F = Bil-siruS

F=buin$Eava--d-(J-Parrrrclo--

Idr^r- of radtoo^t d

AN = NdV

ttL aJevo I^^ fluI ampl = Nto) do

BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

ampB B ordmordmB

b ) (I-Ilt5II7=IIIgt6B8 amp68ordm

131313

times13II(ltII13IIamp$IAI13

BC13I3D5IAIIIampIampDB8E

5IFCGIAIBI35HIGI

I13B13GJordm

13

ordmordmordm

ordmordmordmordm

ordm

b

b

b

b

b

K3I9LIF13M+I131318+B13J$

ordmordm

b INO3Iampamp

b P9 (

b 135IQE13Bordm

b RP9

b S)

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13U(IV8EGIampamp13WXI

ordm ordm

ordm

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b

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b BDjI13aordm

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plusmnG4P913813B13I13I 1kIlGIII

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

Forrnrjc SbteeL fop Gt4aPY B

A ssu^g trtr c-obruafuorc

s= uLL $aV2= +0s

n jnitia sp^LV = ftaf ptlg = 6Ihhwa enuA

Nartong eod Laco i r - lrr

f =rna or7= or F ^u -

1l- ampfJrrtaL e1u-aEot+t vttur -lta- xilvel- + d er x-

lr4r^L[enr-- 4hdL -lt u4 tn4-A tlHilf fiL frot-

is rypfrnfo^ oi + oT v

Iie^rbnl 2A Le iw -b-

TIw do|= 6 Yx+ -Jtuz W ennArnzd ito

wo -fto WJhf -effA^ilrtrt wQ- -

f= nft- n=^^A F6= ^oy

F Ab = P ^ trarnrio fu-dip-

e) rrp- + q^rhfl-kff T ffi bd

b ffrnw-droru -fuEfi^

amp= ryf6ravito[t onaL pd^tiot tt] if ^ ^ 0r a- P6Rt Tl

otho|q- tt^r- Qgnt6g racltue ampr o -

6F8 = -6 El+k-=-icry

frah^v frr drw poulbrv p a puwholo- Lndep cL ra$b^ri tucl

Mea is(= Astdf f e)

-i1 = Awoo+S)

alurutirj ffiT

IF dr4+iuiaL qoh= SY ct

g)= anr6rw vryy = T0^t- ptIAilwt ts

ffi71 +-y-

ltr ffin nnlrU c4^atior ftr cL- Vnau0-$-t$ s6ruhrrt ts

n^n^fr JUgdYfi 6rffitrltrTnamprivc- wu- Silttt elurtrru th^b cgvLhe dpa t^r

cors^fur pt- tut 01^ fr )ttttr o^d- fraF u^oq]

-- F= n^i or --t =Jx

1e -= CDI At-f

drn = al A

zlT

= O

+ T znrftrt-uf-

T= tnrF 1

i+=0coz= L

yn

Kr= rnulContof wlur^ ggf A 6^r

fr^vi+3h =wr$tth

E

t(s-F

P= 4E_db

Kr+ RE C

A

h1v2-

hL

r vut^

r=j-

fr te a satrbvra-nr u tyro- ^drtq$hit Ia-- ts G+$icampl[a-

Flfn pF)= rto) -uf1- -- I Bftz) o-^ urott-n-^ssrin il^ph turif a-t cl

l_lt- ^^ ea-t t cswMvb rrtqnar ff- $^i1t-+ poJ

rfpJ bryat cw +-

pa- pqSrzesvc travoa

d = cto^(t-kq h= +-a

ft= fuspfarurrulb afr aL rrlfuaiL aL ayive-^ poinF i^j ( lndin^

co an5wr ftryt^g of ostltrd^-atuJ oJ fu- prutuclr

(x= dx^rc-- eow ^W fi^uu-uvz- ala^4- lfu x--direthcrn

wampva- wlodtS (u)fZ = fix T= fr = ^tinbt-ktfi = aar crs(3t -kDd

Y - Nasi nt-kf

vrtqxi rlr^nv banttctJl ^eLoci f1 = acc

YvraXirrrrurn pnrrhUr- arc-erdarticr = 4c2

ThB pryakort- relfris lrt ^rnptbn o$ a pcudL irtHrvffvJlxnN-

tD frb cnoh0ru ctf rc- vra-v a

hruot at oxPwtaiun -l

Pl

il_xg

t= b

ts

5e--A ftrw hhD$L evtuvsian

Aa= A(1 ops) f =

hfu-tfrcrrnaL exPaAsiolu I

Vs= U(1+Ye)

ES-

5VY=-v

amps

p=zd -=3d

O fu$swJ

= W ufty yq P$u L^vU ba-

k = -WwrnaL csndunnZ

TWO1 a^d

QD q =rn[-

E=rnctT

f rV)rw qV c a^lfir

i = r

(9Alrr- ^-r fiunL tu--ry ^A ltdirn f er^f-lj^ (- Y

t-J

6tA r J- =- r__ s5r g

Siw uwveninns i

-

fD iS pesitra for ^ cnncLveuro rnirrrof a^LI

ywLt ( o rs is pasibve

v-rrahra]- iofr

ou CffrVOc

a-T

gpepnaL conJuAtm)

k A fg- )7c

=-s F vnalirraS q cnvLaVB Jens] I

urpe- X = disfurr1ap-- rl]rk-cb ampn Sq-nvtC n rtr f

$namp -fi^L obrqf [s re-aL tA naCr-ve

uI

Lg-nSr

l-r I5SDYa

Ngt( -

s infucqlas

fn au hine )ans

t =G 9tt +)frgt= relrmte- uAr o le-os

h r = reurod6+ femampe- LAzx eurotr-frou^e nL

( and A es(w rdn 4 f sa|a qf fl^ JjrJ

RaEutrr^-- -=---- o

^ =_ sln I

5i^ t

rf = L-- uiJL(eL i aeuoaampffirr-

Fk^ficilv c_ __v - _ - a o

$= IR [ovit

fu amp=

[]

t P-xrut]

a s rnaJl urerf rrrrt -

feoU- Sava-tV

P= f V =TR

lA^ i dL x ftv _-4x hz

I)o i Llsin94F YL

hZRr+

ng_t(- Rtl

Laflrrfik- r amp^a- bdu

6n lrl Blr raLw

t4aqrpI^D |4terAr- t^ )w2 etutevtt- -tiltYi9 d9 qL a- l

Adbaha-e- n 4rrrn $r- ^Hc t

z[r

)iuLL oh U^ eu$t- o-- ^ s6b-niAuB

= ry Tf=lra -rturilnh- r+ ry^vL

B=ampt

[aprah-L

naBe4

r^rtrunk

f = --lrf$ ftavA^1a W^r of dtrtnoTamp i-fu

futes- ouv) a- errrant Cgrr$ih t^ri-leuro- rn an ehnA b dzlA

F = Bil-siruS

F=buin$Eava--d-(J-Parrrrclo--

Idr^r- of radtoo^t d

AN = NdV

ttL aJevo I^^ fluI ampl = Nto) do

BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

ampB B ordmordmB

b ) (I-Ilt5II7=IIIgt6B8 amp68ordm

131313

times13II(ltII13IIamp$IAI13

BC13I3D5IAIIIampIampDB8E

5IFCGIAIBI35HIGI

I13B13GJordm

13

ordmordmordm

ordmordmordmordm

ordm

b

b

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K3I9LIF13M+I131318+B13J$

ordmordm

b INO3Iampamp

b P9 (

b 135IQE13Bordm

b RP9

b S)

T8 I9413RP9919-1313I3P13GIamp13

13U(IV8EGIampamp13WXI

ordm ordm

ordm

b ltAElig

b ltAElig

b ltAElig

b ltmiddot

AElig

b ltmiddot

AEligAElig

YI-Ilt5II7=Z4F6+eacute+13GII[

DIG13GBI[RP9]9^[I

E9Jordmordmeacute+ordm

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b 13

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

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ts

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ES-

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amps

p=zd -=3d

O fu$swJ

= W ufty yq P$u L^vU ba-

k = -WwrnaL csndunnZ

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f rV)rw qV c a^lfir

i = r

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t-J

6tA r J- =- r__ s5r g

Siw uwveninns i

-

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v-rrahra]- iofr

ou CffrVOc

a-T

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k A fg- )7c

=-s F vnalirraS q cnvLaVB Jens] I

urpe- X = disfurr1ap-- rl]rk-cb ampn Sq-nvtC n rtr f

$namp -fi^L obrqf [s re-aL tA naCr-ve

uI

Lg-nSr

l-r I5SDYa

Ngt( -

s infucqlas

fn au hine )ans

t =G 9tt +)frgt= relrmte- uAr o le-os

h r = reurod6+ femampe- LAzx eurotr-frou^e nL

( and A es(w rdn 4 f sa|a qf fl^ JjrJ

RaEutrr^-- -=---- o

^ =_ sln I

5i^ t

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Fk^ficilv c_ __v - _ - a o

$= IR [ovit

fu amp=

[]

t P-xrut]

a s rnaJl urerf rrrrt -

feoU- Sava-tV

P= f V =TR

lA^ i dL x ftv _-4x hz

I)o i Llsin94F YL

hZRr+

ng_t(- Rtl

Laflrrfik- r amp^a- bdu

6n lrl Blr raLw

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z[r

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= ry Tf=lra -rturilnh- r+ ry^vL

B=ampt

[aprah-L

naBe4

r^rtrunk

f = --lrf$ ftavA^1a W^r of dtrtnoTamp i-fu

futes- ouv) a- errrant Cgrr$ih t^ri-leuro- rn an ehnA b dzlA

F = Bil-siruS

F=buin$Eava--d-(J-Parrrrclo--

Idr^r- of radtoo^t d

AN = NdV

ttL aJevo I^^ fluI ampl = Nto) do

BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

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131313

times13II(ltII13IIamp$IAI13

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

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$namp -fi^L obrqf [s re-aL tA naCr-ve

uI

Lg-nSr

l-r I5SDYa

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t =G 9tt +)frgt= relrmte- uAr o le-os

h r = reurod6+ femampe- LAzx eurotr-frou^e nL

( and A es(w rdn 4 f sa|a qf fl^ JjrJ

RaEutrr^-- -=---- o

^ =_ sln I

5i^ t

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Fk^ficilv c_ __v - _ - a o

$= IR [ovit

fu amp=

[]

t P-xrut]

a s rnaJl urerf rrrrt -

feoU- Sava-tV

P= f V =TR

lA^ i dL x ftv _-4x hz

I)o i Llsin94F YL

hZRr+

ng_t(- Rtl

Laflrrfik- r amp^a- bdu

6n lrl Blr raLw

t4aqrpI^D |4terAr- t^ )w2 etutevtt- -tiltYi9 d9 qL a- l

Adbaha-e- n 4rrrn $r- ^Hc t

z[r

)iuLL oh U^ eu$t- o-- ^ s6b-niAuB

= ry Tf=lra -rturilnh- r+ ry^vL

B=ampt

[aprah-L

naBe4

r^rtrunk

f = --lrf$ ftavA^1a W^r of dtrtnoTamp i-fu

futes- ouv) a- errrant Cgrr$ih t^ri-leuro- rn an ehnA b dzlA

F = Bil-siruS

F=buin$Eava--d-(J-Parrrrclo--

Idr^r- of radtoo^t d

AN = NdV

ttL aJevo I^^ fluI ampl = Nto) do

BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

rfpJ bryat cw +-

pa- pqSrzesvc travoa

d = cto^(t-kq h= +-a

ft= fuspfarurrulb afr aL rrlfuaiL aL ayive-^ poinF i^j ( lndin^

co an5wr ftryt^g of ostltrd^-atuJ oJ fu- prutuclr

(x= dx^rc-- eow ^W fi^uu-uvz- ala^4- lfu x--direthcrn

wampva- wlodtS (u)fZ = fix T= fr = ^tinbt-ktfi = aar crs(3t -kDd

Y - Nasi nt-kf

vrtqxi rlr^nv banttctJl ^eLoci f1 = acc

YvraXirrrrurn pnrrhUr- arc-erdarticr = 4c2

ThB pryakort- relfris lrt ^rnptbn o$ a pcudL irtHrvffvJlxnN-

tD frb cnoh0ru ctf rc- vra-v a

hruot at oxPwtaiun -l

Pl

il_xg

t= b

ts

5e--A ftrw hhD$L evtuvsian

Aa= A(1 ops) f =

hfu-tfrcrrnaL exPaAsiolu I

Vs= U(1+Ye)

ES-

5VY=-v

amps

p=zd -=3d

O fu$swJ

= W ufty yq P$u L^vU ba-

k = -WwrnaL csndunnZ

TWO1 a^d

QD q =rn[-

E=rnctT

f rV)rw qV c a^lfir

i = r

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BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

O fu$swJ

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f rV)rw qV c a^lfir

i = r

(9Alrr- ^-r fiunL tu--ry ^A ltdirn f er^f-lj^ (- Y

t-J

6tA r J- =- r__ s5r g

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-

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urpe- X = disfurr1ap-- rl]rk-cb ampn Sq-nvtC n rtr f

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uI

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h r = reurod6+ femampe- LAzx eurotr-frou^e nL

( and A es(w rdn 4 f sa|a qf fl^ JjrJ

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^ =_ sln I

5i^ t

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$= IR [ovit

fu amp=

[]

t P-xrut]

a s rnaJl urerf rrrrt -

feoU- Sava-tV

P= f V =TR

lA^ i dL x ftv _-4x hz

I)o i Llsin94F YL

hZRr+

ng_t(- Rtl

Laflrrfik- r amp^a- bdu

6n lrl Blr raLw

t4aqrpI^D |4terAr- t^ )w2 etutevtt- -tiltYi9 d9 qL a- l

Adbaha-e- n 4rrrn $r- ^Hc t

z[r

)iuLL oh U^ eu$t- o-- ^ s6b-niAuB

= ry Tf=lra -rturilnh- r+ ry^vL

B=ampt

[aprah-L

naBe4

r^rtrunk

f = --lrf$ ftavA^1a W^r of dtrtnoTamp i-fu

futes- ouv) a- errrant Cgrr$ih t^ri-leuro- rn an ehnA b dzlA

F = Bil-siruS

F=buin$Eava--d-(J-Parrrrclo--

Idr^r- of radtoo^t d

AN = NdV

ttL aJevo I^^ fluI ampl = Nto) do

BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

ampB B ordmordmB

b ) (I-Ilt5II7=IIIgt6B8 amp68ordm

131313

times13II(ltII13IIamp$IAI13

BC13I3D5IAIIIampIampDB8E

5IFCGIAIBI35HIGI

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timesKI13B13I$O3IIIIAJ$

bYyacutecent sup2

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timesTI13a=13IIQ1$513zIy33 J|13II

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

fn au hine )ans

t =G 9tt +)frgt= relrmte- uAr o le-os

h r = reurod6+ femampe- LAzx eurotr-frou^e nL

( and A es(w rdn 4 f sa|a qf fl^ JjrJ

RaEutrr^-- -=---- o

^ =_ sln I

5i^ t

rf = L-- uiJL(eL i aeuoaampffirr-

Fk^ficilv c_ __v - _ - a o

$= IR [ovit

fu amp=

[]

t P-xrut]

a s rnaJl urerf rrrrt -

feoU- Sava-tV

P= f V =TR

lA^ i dL x ftv _-4x hz

I)o i Llsin94F YL

hZRr+

ng_t(- Rtl

Laflrrfik- r amp^a- bdu

6n lrl Blr raLw

t4aqrpI^D |4terAr- t^ )w2 etutevtt- -tiltYi9 d9 qL a- l

Adbaha-e- n 4rrrn $r- ^Hc t

z[r

)iuLL oh U^ eu$t- o-- ^ s6b-niAuB

= ry Tf=lra -rturilnh- r+ ry^vL

B=ampt

[aprah-L

naBe4

r^rtrunk

f = --lrf$ ftavA^1a W^r of dtrtnoTamp i-fu

futes- ouv) a- errrant Cgrr$ih t^ri-leuro- rn an ehnA b dzlA

F = Bil-siruS

F=buin$Eava--d-(J-Parrrrclo--

Idr^r- of radtoo^t d

AN = NdV

ttL aJevo I^^ fluI ampl = Nto) do

BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

ampB B ordmordmB

b ) (I-Ilt5II7=IIIgt6B8 amp68ordm

131313

times13II(ltII13IIamp$IAI13

BC13I3D5IAIIIampIampDB8E

5IFCGIAIBI35HIGI

I13B13GJordm

13

ordmordmordm

ordmordmordmordm

ordm

b

b

b

b

b

K3I9LIF13M+I131318+B13J$

ordmordm

b INO3Iampamp

b P9 (

b 135IQE13Bordm

b RP9

b S)

T8 I9413RP9919-1313I3P13GIamp13

13U(IV8EGIampamp13WXI

ordm ordm

ordm

b ltAElig

b ltAElig

b ltAElig

b ltmiddot

AElig

b ltmiddot

AEligAElig

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DIG13GBI[RP9]9^[I

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b

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3_I1313`I13a7^13bccc3I_

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ordmordmordm $ordm

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b 13

BI1313I5IDI135I6G

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b BDjI13aordm

b s

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plusmnG4P913813B13I13I 1kIlGIII

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

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BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

BANGLADESH PHYSICS OLYMPIAD

2014

National Round

Category C

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

ampB B ordmordmB

b ) (I-Ilt5II7=IIIgt6B8 amp68ordm

131313

times13II(ltII13IIamp$IAI13

BC13I3D5IAIIIampIampDB8E

5IFCGIAIBI35HIGI

I13B13GJordm

13

ordmordmordm

ordmordmordmordm

ordm

b

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b

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b

K3I9LIF13M+I131318+B13J$

ordmordm

b INO3Iampamp

b P9 (

b 135IQE13Bordm

b RP9

b S)

T8 I9413RP9919-1313I3P13GIamp13

13U(IV8EGIampamp13WXI

ordm ordm

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

National Physics Olympiad 2014

BdPhO Group-C

March 7 2014

Total time - 2hrs Marks -24

You have to show all your intermediate calculations on the pages provided Otherwise you willnot get awards for your efforts

Various Physical Constants

bull Avogadrorsquos Number NA = 602 times 1023 moleminus1

bull electronic charge e = 16 times 10minus19 C

bull Planckrsquos constant h = 663 times 10minus34 J s

1 Heavenly Collisions (total 3 marks)

Two identical heavy point-like objects with mass M each are at rest separated by a distanceD

(a) What is the total energy of the system initially (05 marks )

(b) Find the expression for the speed of the individual particle once they start moving andhave a separation x between them ( 05 marks )

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

ampB B ordmordmB

b ) (I-Ilt5II7=IIIgt6B8 amp68ordm

131313

times13II(ltII13IIamp$IAI13

BC13I3D5IAIIIampIampDB8E

5IFCGIAIBI35HIGI

I13B13GJordm

13

ordmordmordm

ordmordmordmordm

ordm

b

b

b

b

b

K3I9LIF13M+I131318+B13J$

ordmordm

b INO3Iampamp

b P9 (

b 135IQE13Bordm

b RP9

b S)

T8 I9413RP9919-1313I3P13GIamp13

13U(IV8EGIampamp13WXI

ordm ordm

ordm

b ltAElig

b ltAElig

b ltAElig

b ltmiddot

AElig

b ltmiddot

AEligAElig

YI-Ilt5II7=Z4F6+eacute+13GII[

DIG13GBI[RP9]9^[I

E9Jordmordmeacute+ordm

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3_I1313`I13a7^13bccc3I_

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ordmordmordm $ordm

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b 13

BI1313I5IDI135I6G

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gtII13I-gI13-3 3EhsdeR4IBIIiIIS

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ordm s

b BDjI13aordm

b s

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plusmnG4P913813B13I13I 1kIlGIII

8BM13IImGn13Iop$1kIGI8BMIIm(

813B13IBIDIq--GIDI+133B8BM813B13I5I6GJordmordmordmordmordm

ordm 13ordm

ordmordmordmordm

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IIiI13+4(-13I-II789

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b

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times1312ICM+-I9IA138B3 13times]13r

(8B12+sccctA12+Jordmordmordm

ordm

b 13

b

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timestimesI13aI+I9I+3 5I3 3D13u4(59v

134I+3 5I3 53IwBORx5I3 Iy3 Iv

813ordmordm$

ordmordm0

b

b

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b Ob

timesKI13B13I$O3IIIIAJ$

bYyacutecent sup2

d 1

d

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sup2d

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d 1

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d O sup2 1

d

timesTI13a=13IIQ1$513zIy33 J|13II

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b eacuteYd

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timesYI13G513IB13Iy3IIamp13(Iy3

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b uacute2

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timesgtIDIIIIG134II13

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b

timesplusmnB1393WB135I(7894I1313

IA13B13I13UI13BB13135DtimestimesNTtimesII

789II13B13IampIBII1393O

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ordmordmordm

$ordmordmordmordm

b

b 13

b

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times3115eacute413IB13eacute13MDeacuteMDII9IA13

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b 5I

b ltN6

b 134

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

(c) Find the time for them to collide under the influence of mutual gravitational force ( 2marks )

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

ampB B ordmordmB

b ) (I-Ilt5II7=IIIgt6B8 amp68ordm

131313

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

2 Einstein deHass experiment ( Total 5 marks ) (a) Consider a particle of mass m and withcharge q moving with uniform speed in a circle ( as in the Bohr model for hydrogen atom )whose radius is R Then a crude approximation for the current is given by

I = qT

where T is the period of revolution for the charged particle along the circle

Find the relation between the angular momentum of the particle and the magnetic momentof the ldquolooprdquo ( 1 mark)

(b) An unmagnetized iron magnet do not carry any net magnetic moment as all the atomicmagnets are oriented in a random direction However if a strong magnetic field along theaxis of an unmagnetized iron bar the magnetic moments all get oriented ( assuming verylow temperature for the rod) Consider one such iron rod suspended vertically using a veryfine thread and inside a long solenoid which produces a uniform magnetic field inside it ( asshown in the figure ) The white dots denote current going into the plane of the figure whilethe black dots represent current coming out of the plane of the figure In what directionwill the suspended vertical iron rod will rotate if the magnetic field is applied to the rodusing the current configuration shown in the figure ( You might want to state in terms ofangular momentum pointing up of down on the figure ) Provide a physical reason behindyour answer ( 2 Mark)

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

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B13eacute

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$

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131313

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

(c) If the radius of the suspended (cylindrical ) iron bar is R=10 mm estimate T - the periodof rotation of the cylinder Assume that iron atoms each have an orbital angular momentumof ( in accordance with Bohr model ) h equiv h

2π and they become completely alligned in theexternal magnetic field The molar mass of iron is given as M = 00558 kgmol ( 2 marks )

3 Coupled Pendulum (Total 6 marks)

Two identical simple pendula A and B are suspended next to each other from a room wherethe separation between their suspension points is x0 The effective length for each of thependulum is l The point masses are also attached by a massless spring with a spring constantk Let the angular displacements from the vertical position for A and B be θA and θB

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

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B13eacute

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

(a) Evaluate the potential energy of the system as a function of θA and θB assuming thepotential energy to be zero when θA = θB = 0 ( 1 Mark)

(b) Since this is a conservative system the energy of this system will be a constant Differenti-ate the total energy with respect to time t ( noting that both θA θB both vary independentlyas functions of t) and find the equations of motion for the system ( 2 marks )

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

(c) For small oscillations we can replace the trigonometric functions by their Taylor expan-sions Find the oscillation frequencies of this system of double pendula and identify the modesof oscillation ( 3 marks )

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

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131313

times13II(ltII13IIamp$IAI13

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13

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ordm

b

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K3I9LIF13M+I131318+B13J$

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b P9 (

b 135IQE13Bordm

b RP9

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T8 I9413RP9919-1313I3P13GIamp13

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timesKI13B13I$O3IIIIAJ$

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timesTI13a=13IIQ1$513zIy33 J|13II

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b 134

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

4 Blurred Images (Total 3 marks)

An opaque screen has two very narrow parallel slits which are separated by a distance dThe screen is illuminated by a straight bright tube of width W which is placed at a distanceL away from the screen with the parallel slits A filter is placed in between them so thatonly light of wavelength λ falls on the slits Now if one changes the separation between theslits is changed continually then it is found that for d = d0 the interference fringes on theobservation screen placed at a large distance disappears What is the value of W (in termsof other quantities)

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

13ordmeacute

13eacute

I13egrave

b B13II13 I138

$

b ampI(B)+-13012ordmordmordmordmordm

ordmordm$

b I313 II)IampII41356789)+I

ampB B ordmordmB

b ) (I-Ilt5II7=IIIgt6B8 amp68ordm

131313

times13II(ltII13IIamp$IAI13

BC13I3D5IAIIIampIampDB8E

5IFCGIAIBI35HIGI

I13B13GJordm

13

ordmordmordm

ordmordmordmordm

ordm

b

b

b

b

b

K3I9LIF13M+I131318+B13J$

ordmordm

b INO3Iampamp

b P9 (

b 135IQE13Bordm

b RP9

b S)

T8 I9413RP9919-1313I3P13GIamp13

13U(IV8EGIampamp13WXI

ordm ordm

ordm

b ltAElig

b ltAElig

b ltAElig

b ltmiddot

AElig

b ltmiddot

AEligAElig

YI-Ilt5II7=Z4F6+eacute+13GII[

DIG13GBI[RP9]9^[I

E9Jordmordmeacute+ordm

b

b

b

b

b

3_I1313`I13a7^13bccc3I_

IBIB_13`RdeRfccIA`GJ-$

ordmordmordm $ordm

b

b

b

b

b 13

BI1313I5IDI135I6G

Jordm

b 13

b

b

b 13

b 13

gtII13I-gI13-3 3EhsdeR4IBIIiIIS

II3 I13-3 ordmordmordm

ordm s

b BDjI13aordm

b s

b

b s

b s

plusmnG4P913813B13I13I 1kIlGIII

8BM13IImGn13Iop$1kIGI8BMIIm(

813B13IBIDIq--GIDI+133B8BM813B13I5I6GJordmordmordmordmordm

ordm 13ordm

ordmordmordmordm

ordmordm

ordmordmordm

b

b

b

b

b 13

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

5 Freezing and Boiling ( Total 4 marks )

The heat released by the cooling of one mole of H2O from 250 C to 00C and subsequent freezingin a refrigerating machine ( which has the maximum theoretical efficiency) is transferred toa second mole of H2O at 250 C - heating it to 100OC

(a) How many moles of H2O is converted to steam at 100OC( 25 marks )(b) How much work must be done by the refrigerator ( 15 marks )

The latent heat of fusion for H2O is 602 kJmole while the latent heat of boiling for H2O is4068 kJmole

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

6 Data Analysis (Total 3 marks )Given the following set of data find the best graphical fit according to the relationy = Ax2 + b You have to show all your intermediate steps and the results in this page andplot the data in the provided graph sheet in the next page

x 05 1 15 20 25 30y 120 110 235 305 440 550

II13egrave1313

eacuteeacute

13eacute

B13eacute

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

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1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

timestimesI13aI+I9I+3 5I3 3D13u4(59v

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b

b

b Ob

timesKI13B13I$O3IIIIAJ$

bYyacutecent sup2

d 1

d

bYyacutecent sup2

d 1

d O

sup2d

bYyacutecent sup2

d O sup2d

bYyacutecent sup2

d 1

bYyacutecent sup2

d O sup2 1

d

timesTI13a=13IIQ1$513zIy33 J|13II

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b eacuteYd

b eacuteYd b

b

b 2

timesYI13G513IB13Iy3IIamp13(Iy3

IIamp13D133

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b

b

b 13

b

b

timesI13aI+I3 1IIamp134BI51 D3I

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$

b uacute2

b

b dcent1

centd

b uacute13

bdcent12

times8)51 W IBIIuB3A9GS3amp

9IB3A13Jordmordmordm

b

b uacute2

b dcent12

b dcent1

centd

b dcent12

timesgtIDIIIIG134II13

I13IB3A5IB3A131pIamp13D

I13I+13Iordmordm$

ordm

b

timesplusmnB1393WB135I(7894I1313

IA13B13I13UI13BB13135DtimestimesNTtimesII

789II13B13IampIBII1393O

7894I13133 3 IA13J ordmordm

ordmordmordm

$ordmordmordmordm

b

b 13

b

b

b

times3115eacute413IB13eacute13MDeacuteMDII9IA13

IampNSdJ3115eacute4ordmeacute13eacute$ordm

b 5I

b ltN6

b 134

b 5IN]137

b 34

K8)53AIampNSd-13]BI1313I3 4IB

BN4M133 I13GB13GIIAJordmordm

b

b

b

b

b 13

1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

timesI13aI+I3 1IIamp134BI51 D3I

5(B13OIamp1351 W1pM+13Jordmordmordm

$

$

b uacute2

b

b dcent1

centd

b uacute13

bdcent12

times8)51 W IBIIuB3A9GS3amp

9IB3A13Jordmordmordm

b

b uacute2

b dcent12

b dcent1

centd

b dcent12

timesgtIDIIIIG134II13

I13IB3A5IB3A131pIamp13D

I13I+13Iordmordm$

ordm

b

timesplusmnB1393WB135I(7894I1313

IA13B13I13UI13BB13135DtimestimesNTtimesII

789II13B13IampIBII1393O

7894I13133 3 IA13J ordmordm

ordmordmordm

$ordmordmordmordm

b

b 13

b

b

b

times3115eacute413IB13eacute13MDeacuteMDII9IA13

IampNSdJ3115eacute4ordmeacute13eacute$ordm

b 5I

b ltN6

b 134

b 5IN]137

b 34

K8)53AIampNSd-13]BI1313I3 4IB

BN4M133 I13GB13GIIAJordmordm

b

b

b

b

b 13

1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

timesplusmnB1393WB135I(7894I1313

IA13B13I13UI13BB13135DtimestimesNTtimesII

789II13B13IampIBII1393O

7894I13133 3 IA13J ordmordm

ordmordmordm

$ordmordmordmordm

b

b 13

b

b

b

times3115eacute413IB13eacute13MDeacuteMDII9IA13

IampNSdJ3115eacute4ordmeacute13eacute$ordm

b 5I

b ltN6

b 134

b 5IN]137

b 34

K8)53AIampNSd-13]BI1313I3 4IB

BN4M133 I13GB13GIIAJordmordm

b

b

b

b

b 13

1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

1 একটি a দৈঘযবিবলষট সমবাহ টিভজের দই শীজষে দটি ভর M রাখা আজে এবং অনয শীজষে আররকবি

ভর m রাখা আরে [Mass points M and m are kept at the vertices of an equilateral triangle

whose sides are of length a]

a) m ভর রে বরেরের ভররকরের ৈরতব বির কর [ Find the distance between the center

of mass of the system and mas point m ] ( 2 marks )

b) ভররকরের ারেরে বরেরের জড়োর ভরােক বিরয় কররা [ Determine the moment of

Inertia of the system about the center of mass ] ( 15 marks )

2 a) াইররারজি বিউবিয়ারর চারোরল ইরকটররির েবরিরে যবৈ েযযয়ি ( muon) করা েবরভরের করর

েরি এই েযযয়বিক াইররারজরির জিয বিার িযাারধর বিরয় করার জিয পররযাজিীয় েীকরি বির

কররা েযযয়ি করার ভর ইরকটররির ভররর ২৩৬ গি এিং এর চাজ ইরকটররির চারজর োি [The muonic hydrogen consists of a muon encircling the hydrogen nucleus Find the

expression for determining the Bohr radius of this muonic hydrogen The mass of muon

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

is 236 times that of the electron and it carries the same charge as electron] (me = 91 x

10-31

kg e= 16 x 10-19

C h= 662x10-34

Js ) ( 2 marks)

b) েযযয়বিক াইররারজরির জিয বিার িযাারধর োি কে [ What is the numerical value of the

Bohr radius for the muonic hydrogen ] ( 1 Mark)

c) এই েযযয়বিক াইররারজি েরোরযরক ের আযবিে কররে কে বভালট বিভি পররয়াজি [ What is

the ionization potential for this muonic hydrogen ] ( 1 Mark )

3 একবি িগাকবের চেয ভয রজর চারবি েযায়করবেক িাহর বরাধ R 2R 2R R এিং পররেযক িাহর দৈঘয L

R ও 2R বরাধবিবলষট িাহগবর বয ৈযবি বিনদযরে বেবে য় (ধরা যাক বগরার িাে A ও B ) ব ৈযrsquoবি

বিনদযর োরে V বিভি োরকয পররয়াগ করা রা [ Consider a square whose successive sides of

length L has resistances R 2R 2R R respectively If a potential difference V is applied

between the points (call them say A and B) where the sides with R and 2R meet]

a) িাহগবরে েবড়ৎ পরিারর োি বির কররা [ Find the currents in the individual sides of

the square ] ( 1 mark )

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

b) িরগর বকরে B বেরের োি বিরয় কররা [ Find the B field at the center of the square ] ( 3

Marks)

c) যবৈ একই বিভি োরকয A ও B এর েবরিরে অিয ৈযই বিনদযর োরে পররয়াগ করা য় োর

উেররর উততররর বক বকারিা েবরিেি য় উততররর েরে যযবি ৈাও [ If now the same

potential applied in the remaining pair of vertices instead of A and B then will there

be any change in the answers obtained above Justify your answer ] ( 2 Marks )

4 M ভর ও L দৈরঘযর একবি র বৈাকরক E োরির উরধেযখী একবি যে দিৈয যবেক িরেরে রাখা

রা [ A simple pendulum of mass M and length L is kept in a uniform electric field E

which points upward]

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

a) র বৈারকর েয নত ভরর Q েবরোর চাজ বৈয়া র র বৈারকর বৈািকা বির কর [ If a

charge Q is deposited on the suspended mass find the period of the oscillation of the

simple pendulum ] ( 2 Marks)

b) Q এর োি কে র বৈাকবি আর ৈযরি িা[ For what value of Q will the pendulum

stop oscillating ] ( 1 Mark )

5 একবি োনতরা োে ধাররকর োরের োরের ৈরতব d ও োরের পরসথরেৈ A এখি চাজলিয

অিসথায় ধাররকর ৈযপরারনত V েবড়ৎ চাক িরর একবি িযািারীর ারর যযি করা রা [ A parallel

plate capacitor has a plate separation of d and plate cross section A The two ends of

capacitor are now connected to a battery of EMF V while being initially uncharged ]

a) িযািারীবক বিবেনন করর োরের োরের ৈরতব চারগর িবি কররে বক েবরোর কাজ কররে রি [ What would be the work done to separate the plates by a factor of 4 if the capacitor is

separated from the battery after initial charging] ( 1 Mark)

b) িযািারীরক বিবেনন িা করর কারজর েবরোর বক একই রাকরি িা েবরিবেে রি

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

েবরিবেে র বক েরির েয িায় িড় িা বোি উততররর েরে িযাখযা ৈাও [ If the battery

remains connected during the above process will the work done be any different If

different will the work be greater or less than the disconnected case Justify your

answer ] ( 25 Marks )

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

1 Given the acceleration vs time graph for a car shown above at what time will be moving with the greatest velocity A) 0 seconds B) 2seconds C) 4 seconds D) 6 seconds E) 8 seconds 2 A car is moving at a constant velocity to the right along a straight level highway Just as the car passes a cliff a rock falls straight down in the cliffrsquos reference system Which of the accompanying curves best depicts the path the rock takes in the carrsquos reference system

A) B) C) D) E)

3 Two identical masses m are connected to a massless string which is hung over two frictionless pulleys as shown

If everything is at rest what is the tension in the cord A) Less than mg B) Exactly mg C) More than mg but less than 2mg D) Exactly 2mg E) More than 2mg 4 A 60 kg farmer ropes a 300 kg ox Both are initially at rest 24 m apart on a frictionless level surface When farmer ends up pulling the ox towards him the ox will move A) 4m B) 5m C) 12m D) 20m E) 24m

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

5 A small bird with a mass of 05 kg takes off from the ground and flies with an upward velocity of 3 msec for 10 seconds Which of the following is closest to the minimum power that must be developed by the bird A) 60 watts B) 15 watts C) 9 watts D) 6 watts E) 15 watts 6 A solid cylinder weighing 200 N has a fixed axis and a string wound around it The string is pulled with a force equal to the weight of the cylinder The acceleration of the string is approximately13 13 A) 10 ms2 B) 20 ms2 C) 30 ms2 D) 40 ms2 E) 50 ms2 13 7 A ball of mass m is tied to a string The ball is then rotated in a vertical circle of radius R with the other end of the string fixed Neglecting air resistance the difference between the stringrsquos tension at the bottom of the circle and the top of the circle is A) mg B) 2mg C) 4mg D) 6mg E) 8mg 8 Suppose you hold a ball in your hand The Newtonrsquos third law companion force to the force of gravity on the ball is the force exerted by the A) Ball on the Earth B) Ball on the hand C) Hand on the ball D) Earth on the ball E) Earth on the hand 9 A ball is tossed straight up reaches a highest point and falls back down Air resistance is not negligible Which of the following statements are true13 13

I) The balls speed is zero at the highest point13 II) The balls acceleration is zero at the highest point 13 III) The ball takes longer time to travel up to the highest point than to fall back

down13 13 A) I only B) II only C) I amp II only D) I amp III only E) III amp III13 13 10 Two iron spheres separated by some distance have a minute gravitational attraction F If the spheres are moved to one half their original separation and allowed to rust so that the mass of each sphere increases 41 what would be the resulting gravitational force A) 2F B) 4F C) 6F D) 8F E) 10F

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

11 A block of ice with mass m falls into a lake After impact a mass of ice m5 melts Both the block of ice and the lake have a temperature of 0o C If L represents the heat of fusion the minimum distance the ice fell is A) L5g B) 5Lg C) gL5m D) mL5g E) 5gLm

12 On all the PV diagrams shown above the lighter curve represents an isothermal process a process for which the temperature remains constant Which dark curve best represents an adiabatic process where no heat enters or leaves the system A) B) C) D) E)

1313 13 For13 the13 diagram13 given13 above13 what13 is13 the13 efficiency13 of13 the13 heat13 engine13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 13 13 13 A)13 30013 B)13 13313 C)13 7513 D)13 3313 E)13 2513 13 14 If heat is added at constant volume 6300 joules of heat are required to raise the temperature of an ideal gas by 150K If instead the heat is added at constant pressure 8800 joules are needed for the same temperature change When the temperature of the gas changes by 150K the internal energy of the gas changes by 13 13 A) 2500J B) 6300J C) 8800J D) 11300J E) 15100J13 15 One object has twice the temperature of a second identical object How does the rate R1 at which the first object radiates energy compare to the rate R2 at which the second object radiates energy A) R1 =R2 B) R1 =2R2 C) R1 =4R2 D) R1 = 8R2 E) R1 =16R2

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

16 A pipe which is open at both ends resonates with fundamental frequency 300 Hz If one end of the pipe is closed it will resonate with a fundamental frequency of A) 75 Hz B) 150 Hz C) 300 Hz D) 600 Hz E) 1200 Hz 17 A wave is described by the equation y(xt) = 005 cos ( 10 π x + 8 π t) where x and y are in meters and t is in seconds The +x direction is to the right What is the velocity of the wave

A) 080 ms to the left B) 125 ms to the right C) 012π ms to the right D) 080 ms to the right E) 125 ms to the right

18 The length of the most effective transmitting antenna is equal to one-quarter the wavelength of the transmitted wave If a radio station has an antenna 45 m long then what is the broadcast frequency of the radio station A) 15 x 10-8 Hz B) 60 x 10-8 Hz C) 17 x 107 Hz D) 67 x107 Hz E) 3 x108 Hz 19 You are given two identical Plano-convex lens When an object is placed 20 cm to the left of a single such lens the image appears 40 cm to the right of the lens Then you decide to form a double convex lens by placing the two Plano-convex lenses back-to-back

If an object is placed 20 cm to the left of this new lens the image is formed at a distance

A) 67cm to the right of the lens B) 10 cm to the right of the lens C) 20 cm to the right of the lens D) 80 cm to the right of the lens E) 80 cm to the left of the lens

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

The questions 20 and 21 refer to the system shown in the accompanying diagram A spherical shell of inner surface radius a and an outer surface radius b is made of conducting material A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell 13 13

13 13

20 How is the charge -q distributed after it has reached equilibrium13 13 A) Zero charge on the inner surface -q charge on the outer surface 13 13 B) -Q charge on the inner surface -q charge on the outer surface13 13 C) -Q charge on the inner surface -q+Q charge on the outer surface13 13 D) +Q charge on the inner surface -q -Q charge on the outer surface13 13 E) The -q charge is spread uniformly between the inner and outer surface13 13 21 Assume that the electrostatic potential is zero at an infinite distance from the shell What is the electrostatic potential at a distance R from the center of the shell where b gt R gt a 13 13 A) 0 B) k Qa C) k QR D) k (Q-q)R E) k (Q-q)b13 13 13 22 An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V Which of the following potential differences would be needed to give the alpha particle twice the velocity A) 7200V B) 4800V C) 4100V D) 2400V E) 1700V 13

23 An alpha particle and a proton are placed equal distance between two large charged plates as shown in the figure

Which of the following would best describe the motion of the two particles if they were free to move

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

A) The alpha particle will travel upwards with the twice the velocity of the proton B) Both particles will travel upwards with the same velocity C) The alpha particle will accelerate upwards with twice the acceleration of the

proton D) Both particle will accelerate upwards with the same acceleration E) The alpha particle will accelerate upwards with half the acceleration of the proton 24 The longest wavelength photon in the visible Balmer series for the hydrogen atom is A) 066 nm B) 656 nm C) 656 nm D) 656 nm E) 6560 nm 25 Which of the following wiring diagrams could be used to experimentally determine R using Ohmrsquos law Assume an ideal voltmeter and an ideal ammeter

A 9-volt battery is connected to four resistors to form a simple circuit as shown below

26 What would be the current at point E in the circuit A) 2amp B) 4amp C) 5amp D) 7amp E) 9amp 27 What would be the potential at point B with respect to point D A) +2V B) +4V C) +5V D) +7V E) +9V

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

28 The most common isotope of Uranium 23892U radioactively into 206

82 Pb Lead through a series of alpha and beta particle emissions How many of each particle must be emitted A) 32 alphas and 10 betas B) 16 alphas and 16 betas C) 16 alphas and 8 betas D) 8 alphas and 6 betas E) 4 alphas and 16 betas

29 Identical currents flow in two perpendicular wires as shown in the accompanying figure The wires are very close but do not touch ( you can think of them being insulated)

The magnetic field can be zero A) At a point in region 1 only B) At a point in region 2 only C) At points in both regions 1 and 2 D) At points in both regions 1 and 4 E) At points in both regions 2 and 4 30 A wire moves with a velocity v through a magnetic field and experiences an induced charge separation as shown in the figure

What is the direction of the magnetic field A) Into the page B) Out of the page C) Towards the bottom of the page D) Towards the right E) Towards the top of the page

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

Second13 Round13 Question13 13 (13 4513 or13 6013 minutes13 )13 13 13 5013 marks13 13 13 Show13 all13 your13 work13 in13 the13 pages13 provided13 13 Donrsquot13 forget13 to13 write13 your13 name13 and13 your13 academic13 institution13 13 13 13 113 13 A13 Simple13 pendulum13 as13 shown13 in13 the13 figure13 has13 a13 period13 T13 of13 10013 s13 13

13 a) Calculate13 the13 length13 L13 13 of13 the13 pendulum13 13 b) A13 small13 horizontal13 rod13 is13 now13 placed13 at13 a13 distance13 L213 below13 the13 point13 of13 13

suspension13 of13 the13 pendulum13 13

13 The13 string13 collides13 with13 the13 rod13 once13 in13 each13 oscillation13 Calculate13 the13 new13 period13 Trsquo13 of13 the13 pendulum13 13 13 13 13 13 13 13 13 13 [713 points]13 13

13 2 A white light shines vertically down on a horizontal CD ROM disc A person whose eye is at a horizontal distance 050 m from the disc and 035 m vertically above its horizontal plane views the disc A yellow light of wavelength 590 nm is observed due to first order diffraction a) Deduce the spacing d between adjacent tracks of the CD ROM The CD ROM is

tilted clockwise through an angle of 5o b) Determine the wavelength now observed13

13 13

13 (1213 points)13

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

3 A metal ring of mass m radius r with a small radius of the cross sectional area and resistance R falls symmetrically from rest at time t = 0 in a horizontal radial magnetic field of magnitude B At time t it has a vertical velocity v an acceleration a and a current I

a) Show that due to the rate at which the magnetic flux is cut the current induced on the ring is

I= 2π r Bv R b) Deduce that ma = mg ndash (2π r B)2vR c) Derive the initial variation of v with t Also find the terminal velocity of the ring d) Sketch13 graphically13 the13 variation13 of13 a13 and13 v13 with13 t13 13 13 13 (13 1013 points13 )13 4 Determine the current I through the ammeter A in each of the four circuits in the figures below The ammeter has zero resistance The voltmeter in (ii) has infinite resistance and a reading 8V The resistance R has not been specified

(6 points )

13

N13

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

513 13 This13 question13 comprises13 of13 several13 independent13 parts13 13 13 A13 star13 which13 is13 more13 massive13 than13 our13 sun13 typically13 collapses13 under13 its13 own13 gravity13 to13 form13 neutron13 stars13 13 In13 this13 case13 the13 electrons13 collapses13 into13 the13 nucleus13 and13 form13 neutrons13 after13 fusing13 with13 protons13 13 Stars13 that13 are13 initially13 rotating13 will13 rotate13 faster13 after13 the13 collapse13 due13 to13 the13 conservation13 of13 angular13 momentum13 Let13 us13 recall13 that13 angular13 momentum13 is13 given13 by13 J13 =13 R2Ω13 (omitting13 some13 constants)13 where13 R13 is13 the13 radius13 of13 the13 star13 and13 Ω13 is13 the13 angular13 rate13 of13 rotation13 in13 radians13 per13 second13 13 13 a) If13 the13 volume13 of13 the13 star13 decreases13 by13 1513 orders13 of13 magnitude13 and13 the13 shape13

of13 the13 star13 remains13 the13 same13 then13 what13 is13 the13 ratio13 of13 the13 final13 to13 initial13 radii13 13 Rfinal13 13 Rinitial13 13

b) If13 the13 rotation13 period13 of13 star13 before13 the13 collapse13 was13 2013 days13 calculate13 the13 new13 period13 of13 rotation13 in13 seconds13 and13 also13 Ωfinal13 13

c) 13 When13 the13 core13 of13 the13 star13 collapses13 to13 form13 neutron13 star13 the13 electrical13 conductivity13 becomes13 very13 high13 In13 this13 case13 the13 starrsquos13 magnetic13 field13 becomes13 frozen13 into13 the13 material13 of13 the13 star13 and13 collapse13 down13 with13 the13 star13 increasing13 the13 flux13 density13 The13 resulting13 neutron13 stars13 therefore13 have13 very13 strong13 magnetic13 field13 associated13 with13 them13 If13 the13 magnetic13 field13 for13 the13 star13 before13 the13 collapse13 is13 10-shy‐213 T13 determine13 the13 final13 magnetic13 field13 strength13 near13 the13 surface13 of13 the13 resulting13 neutron13 star13 13 13

d) If13 the13 neutron13 star13 spins13 too13 fast13 it13 will13 start13 losing13 material13 from13 its13 equatorial13 region13 Show13 that13 this13 implies13 a13 minimum13 period13 Tmin13 given13 by13 13 13

Tmin13 =13 radic13 M-shy‐1213 R2313

13 13 13 13 13 13 Taking13 M13 =13 1413 Solar13 Masses13 and13 R=13 1013 km13 find13 13 Tmin13 13 13 13 13 13 13 13 (Note13 Solar13 Mass=2013 x13 103013 kg)13 13 e)13 13 The13 binding13 energy13 of13 a13 neutron13 star13 is13 the13 gravitational13 potential13 energy13 lost13 when13 it13 is13 formed13 from13 a13 cloud13 of13 atom13 all13 separated13 at13 far13 distances13 apart13 The13 binding13 energy13 of13 a13 star13 of13 mass13 M13 and13 radius13 R13 is13 given13 by13 U=13 k113

13 where13 k113 is13 a13 numerical13 constant13 The13 behavior13 of13 the13 neutron13 stars13 is13 quite13 different13 from13 ordinary13 matter13 and13 they13 satisfy13 the13 mass-shy‐radius13 relationship13 given13 by13 RM13=13 k213 with13 k213 being13 another13 numerical13 constant13 13 Now13 assume13 two13 neutron13 stars13 of13 identical13 mass13 fuse13 and13 form13 another13 more13 massive13 star13 13 Assuming13 the13 mass-shy‐radius13 relationship13 to13 be13 valid13 in13 this13 process13 what13 is13 13 the13 ratio13 of13 the13 final13 binding13 energy13 of13 the13 star13 to13 the13 total13 initial13 binding13 energy13 13 13 (1513 marks)13 13 13

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

Group-C (Chittagong division)

Answer all of the following If the exact number is not given pick the answer that is the closest to the

correct answer (Choose c=3x108

ms e=16 x 1019

C h=662x10-34

Js g=98ms2)

1) A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp which is at an angle 30o

above the horizon A linear spring whose length is not negligible is attached to the bottom of the

ramp The ball is released from a distance of 1 m above the spring measured along the plane and

the spring constant is 1Nm then the spring is depressed by

a) 16m ( Answer)

b) 18m

c) 05m

d) The answer cannot be determined from the given data

e) 2m

2) In a sporting meet a hammer thrower spins a mass of 5 kg attached to a chain of 1m length at a

frequency of 075 revolutions per second What is the tension in the chain

a) 100N

b) 200N

c) 110N ( Answer)

d) 150N

e) 130N

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

3) What is the power spent by the athlete to rotate the ldquohammerrdquo

a) 1 Watt

b) 20Watt

c) 100 Watt

d) 0 Watt ( Answer)

e) 2 Watt

4) A hunter sees a monkey at a height 5m hanging from a horizontal branch of a tree which is 10 m

away and thus aims to shoot it with a tranquilizing dart whose muzzle speed is 200ms The clever

monkey sees the hunter and drops vertically downward right at the moment the dart escapes the

hunterrsquos gun What happens then after

a) The monkey escapes

b) The dart hits the monkey (Answer)

c) The hunter should get a gun with higher muzzle speed

d) The hunter should get a gun with lower muzzle speed

e) This cannot be determined as this is not a physics problem

5) An elevator lift is being lifted up an elevator shaft at a constant speed by a steel cable All frictional

effects are negligible In this situation forces on the elevator are such that

(a) the upward force by the cable is greater than the downward force of gravity

(b) the upward force by the cable is equal to the downward force of gravity ( Answer)

(c) the upward force by the cable is smaller than the downward force of gravity

(d) the upward force by the cable is greater than the sum of the downward force of gravity and a

downward force due to the air

(e) none of the above (The elevator goes up because the cable is being shortened not because an

upward force is exerted on the elevator by the cable)

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

6) A woman exerts a constant horizontal force on a large box As a result the box moves across a

horizontal floor at a constant speed ldquov 0rdquo The constant horizontal force applied by the woman

a) has the same magnitude as the weight of the box

b) is greater than the weight of the box

c) has the same magnitude as the total force which resists the motion of the box ( Answer)

d) is greater than the total force which resists the motion of the box

e) is greater than either the weight of the box or the total force which resists its motion

7) If the woman in the previous question doubles the constant horizontal force that she exerts on the

box to push it on the same horizontal floor the box then moves

a) With a constant speed that is double the speed ldquov 0rdquo in the previous question

b) With a constant speed that is greater than the speed ldquov 0rdquo in the previous question but not

necessarily twice as great

c) For a while with a speed that is constant and greater than the speed ldquov 0rdquo in the previous

question then with a speed that increases thereafter

d) For a while with an increasing speed then with a constant speed thereafter

e) With a continuously increasing speed ( Answer)

8) Think of an ideal gas contained inside a vessel which has a piston on its side so that the volume of

the gas inside can be changed but the gas cannot escape We have a pressure gauge in the system

The temperature of the surrounding in fixed on any day and an experimenter measures the pressure

of the gas by varying the volume of the gas by pushingpulling the piston The experimentalist plots

the pressure against the volume recorded in the experiments that are recorded over a week The

temperatures recorded in those days are not equal to each other What is the observation regarding

the graphs

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

a) They are straight lines crossing each other

b) They are concentric circles

c) They are parallel straight lines

d) They are non intersecting hyperbolas ( Answer)

e) They are non intersecting parabolas

9) A person is standing in front of a large and high wall which is 100m away and holds a microphone

that is emitting a loud sound of frequency 110 Hz After moving forward a few paces towards the

wall the person finds a spot where the perceived sound is minimized How much further the person

should move forward so that again the sound is minimized again (The speed of sound can be taken

to be equal to 330 ms)

a) 15m (Answer)

b) 75m

c) 3m

d) 6m

e) 1m

10) Electromagnetic waves are transverse waves Which of the following phenomenon supports this

fact

a) Interference

b) Refraction

c) Reflection

d) Polarization ( Answer)

e) Diffraction

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

11) The plane interface between two transparent media which we call A and B is illuminated whose

refractive indices are 12 and 16 respectively Light will be reflected from the interface as it moves

from B to A at an incident angle greater than

a) 30 degrees

b) 60 degrees

c) 15 degrees

d) 10 degrees

e) 50 degrees ( Answer)

12) To improve the transmission of their program a radio broadcasting company decides to install two

identical transmission towers which are separated by 10 m in the North ndash South direction Both the

towers are fed by a transmission line which feeds the antenna with a signal of frequency 15 x108Hz

The received signal is strongest along the east ndashwest direction The next strongest signal points

along

a) North-South

b) 100 from east-west (Answer)

c) 300 from east-west

d) 700 from north-south

e) 450 from east-west

13) Consider a battery of internal resistance 1 Ohm and EMF 24V connected to a coil of resistance 19

Ohms What is the Voltage that one measures at the end points of the coil

a) 23V (Answer)

b) 22V

c) 21V

d) 20V

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

e) 24V

14) If one has the choice of changing the coil so that it emits the maximum joule heat across it then one

should choose a coil whose resistance is

a) 5 Ohm

b) 40 Ohm

c) 11 Ohm (Answer)

d) 5 Ohm

e) This cannot be determined

15) A 3 m long rod made of copper and held horizontally is suddenly dropped vertically from the

height of 10m while pointing along north-east direction The horizontal component of the Earthrsquos

magnetic field is 10-3

T is that point What is the maximum possible voltage induced across the

copper rod

a) 1 mV

b) 2mV

c) 4mV

d) 5mV

e) 3mV (Answer)

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

16) Consider a circuit shown in the accompanying figure where the resistances are shown What is the

equivalent resistance across the points A and B

a) 2R

b) 1 R

c) 3R

d) 15R (Answer)

e) 7R

17) To ldquoseerdquo atoms one should use electromagnetic radiation ( light ) from the frequency range

a) 1018Hz (Answer)

b) 1020Hz

c) 1012Hz

d) 1014Hz

e) 1016Hz

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

18) A metal is radiated with a light of wavelength 300nm If the work function for the metal is 5eV the

maximum energy of the ejected electron is

a) 1eV

b) Electrons wonrsquot be emitted (Answer)

c) 2eV

d) 5eV

e) 12eV

19) The ionization energy of Hydrogen atom is -136 eV A rough value of the Voltage difference

required for ionizing Helium singly ( that is too strip off a single electron from its orbit ) is around

a) 10V

b) 5V

c) 35V

d) 60V

e) 25V (Answer)

20) Which of the following particles is not a fundamental particle

a) Electron

b) Muon

c) Neutrino

d) Neutron (Answer)

e) Photon

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

িবিভিবিভিবিভিবিভ েভৗতেভৗতেভৗতেভৗত বেকরবেকরবেকরবেকর মানমানমানমান ( Different Physical Constants)

c= 3x108ms h=66x10-34 Js e=16x10-19 C

me ( ইেলকেনর ভর electron mass ) = 91 x 10-31kg

mp ( োটেনর ভর proton mass ) = 16 x 10-27kg

Barisal Division Category-C

১ একিট সরল েদালেকর ববেক ভিমর সমারাল তল বরাবর ω েকৗিণক েবেগ একিট বপেথ েঘারােনা হে$ বের

বাসাধ r এবং বেবর ভর M হেল েদালেকর সতায় টান কত (The bob of a simple pendulum is rotating on a

circle with an angular frequency ω on a horizontal plane If the radius of the circle is r and the mass of the bob is M what is the tension on the rope of the pendulum)

a) Mg b) Mω2r c) M [ ( ω2r)2 + g2 ]12 d) M (ω2r + g)

e) িনণয় করা স-ব নয় ( cannot be determined )

২ ধরা যাক একিট বন হািত িত েসেকে2 ৫ িম েবেগ ধাবমান অব5ায় বায়েত ভাসমান িক7 ি5র এক মািছেক আঘাত

করেলা মািছিট কত েবেগ িছটেক পড়েব (Consider a feral elephant that charges a hovering stationary fly with

a speed of 5ms at a hovering fly What is the speed with which the fly will recoil ) a) 0 ms b) 5ms c) 20ms d) 10ms

e) িনেণয় নয় ( Indeterminate )

৩ েকপলােরর িltতীয় সgt আদেত িনের েকান নীিতর ফলAিত (Which of the following laws leads to the second

law of Kepler )

a) শিCর িনততার সgt ( Conservation of Energy )

b) ৈরিখক ভরেবেগর িনততার সgt ( Conservation of linear momentum)

c) বেলর এটা একিট েমৗিলক Fীকায ( The Keplerrsquos 2nd law is itself a fundamental law )

d) মাধাকষন বেলর িনততার কারেণ ( Conservation of Gravity )

e) শন বল Hামেকর কারেণ ( Due to zero torque )

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

৪ যিদ েকােনা ইেলJনেক একিট কােথাড ের িটউেবর মেধ 3000 েভাM িবভব পাথেকর মাঝ িদেয় চালনা করা হয়

তাহেল ইেলJনিট েথেক সেবাP কত কQােRর েফাটন িবিকিরত হেত পাের (If an electron is accelerated within a

Cathode Ray Tube (CRT) using a voltage difference of 3000 V then what is the maximal frequency for the photon that can be radiated from the electron)

a) 300 x 10 3 GHz b) 750 x10 3 GHz c) 500x 106 MHz d) 750 MHz e) 6000 MHz

৫একজন পারাTট জাQার একিট িবমান হেত ভিম লU বরাবর লাফ িদেলা ধরা যাক বায়র বাধার কারেণ উVত বল

জাQােরর েবেগর সমানপািতক জাQােরর পতেনর েবগ সমেয়র সােথ িকভােব পিরবিতত তা েকান িচgtিট কাশ কের

(A parachute jumper jumps vertically from an aircraft Let the drag force due to air resistance be

proportional to the velocity of the jumper Which of the following graphs describe the variations of the velocity of the jumper with respect to time )

a) b) c) d) e)

৬ ইকিথয়ন নােমর এক িব^ানী D বাসােধর এবং ব ঘন_ ρ মােনর িবটা জাই (βξ) নােমর এক `েহ বাস কেরন

িতিন তার েরাবট বািহনী িদেয় `েহর অভের d ( েযখােন d lt D ) বাসােধর `েহর সমেকিaক একিট গbর ৈতরী

কেরন এখন `হপc হেত h উPতায় অনভত উC `েহর অিভকষজ _রণ কত ( Ichthyion a mad scientist lives

on planet Beta-Xi (βξ) which has a radius D and a constant density ρ He now employs his robot army to dig a spherical hollow which has a radius d lt D and whose center coincides with that of Beta-Xi What is now the gravitational acceleration due to the planet at a height h above the planet surface )

a) 4 ρ π G d3 3 h2 b) 0

c) 4 π G ρ ( D3 ndash d3 ) 3 (D+h)2

d) 4 ρ π G D3 3 h2

e) 4 ρ π G d2 3 D3

৭ (উপেরর েf) যিদ `হেকa েথেক মাপা দর_ x হয় তাহেল x এর মান পিরবতেনর সােথ g এর মােনর পিরবতন

িনেচর েকান `াফ িদেয় সিঠক ভােব কাশ করা স-ব (If x is the distance measured from the center of the

planet Beta-Xi which of the following graphs describe the variation of g with respect to x as described in the previous problem )

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

a) b) c) d) e)

৮ শj িনের েকান সgt বা নীিত েমেন চেল না (Which of the following laws are not obeyed by sound)

a) িতফলেনর সgt ( Laws of reflection)

b) িতসরেণর সgt ( Laws of refraction )

c) অপবতেনর নীিত ( Laws of Diffraction )

d) হাইেগেনর নীিত ( Huygenrsquos principle )

e) সমবতেনর সgt ( Laws of Polarization )

৯ mবm একই রকেমর রাবার েবলেন সমান তাপমাgtা ও বায় চােপ িবিভ গাস রাখা আেছ এেদর মেধ েকান গােস ভরা

েবলনিট সবেচেয় oতহাের চপেস েযেত থাকেব (If identical rubber balloons are inflated with gases kept at the

same temperature and pressure then the balloon containing which gas will deflate the fastest)

a) অিpেজন ( Oxygen )

b) আগন ( Argon )

c) নাইোেজন ( Nitrogen )

d) হাইেqােজন ( Hydrogen )

e) েrািরন ( Chlorine )

১০ পািনর tটেনর সuতােপর মান 2260 JKg 100o েসলিসয়াস তাপমাgtার 2 েকিজ পািনেক বাীভত করেল

এনোিপর কত পিরবতন হেব (The Latent heat of Boiling for Water is 2260 JKg If 2 kg water at 100o

Celsius is boiled then what is its change in entropy)

a) 10 SI units b) 20 SI units c) 4520 SI units d) 450 SI units e) 0 SI units

১১ আদশ গােসর জন িনেচর েকান বCবিট সত (Which of the following statements is true for Ideal gases)

a) Cp gt 0 Cv lt 0 b) Cp gt Cv gt 0 c) Cv gt Cp gt 0 d) Cp lt 0 Cv gt 0 e) Cp gt 0 Cv lt 0

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

১২ িনেচর বতনীেত A ও B িবর মােঝ সমতল েরাধ কত (What is the equivalent resistance between the

points A and B in the following circuit)

a) R b) R2 c) 2R3 d) 3R2 e) 0

১৩ a বাসােধর ও r েরােধর একিট বাকার তামার িরংেক B েচৗUক াবেলর েেgtর মেধ ω েকৗিণক েবেগ ভিমর

সমারাল একিট অের চারিদেক ঘরােনা হে$ িরং-এর মােঝ আিব সেবাP তিড় চালক বেলর মান কত ( A

circular copper ring of radius a and with resistance r is being rotated with an angular frequency ω about

an horizontal axis What is the maximum value of the induced EMF ) a) ωa2

π B b) a2

π Bωr c) 0 d) ωa2

π e) ω B

১৪ উপেরর েfর িরংিটেক েঘারােনার জন িত েসেকে2 গেড় কতটক কাজ করা েয়াজন ( What is the power

required to rotate the ring in the above question ) a) a4

π2 B2 ω2 r

b) 0 c) a4

π2 B2 ω2 2r

d) a4 π

2 B2 ω2 e) a4

π2 B2 ω2 2

১৫ ১০ Tesla াবেলর েচৗUক েেgt োটেনর আবতেনর েকৗিণক েবগ কত (What is the angular velocity of the

orbital motion of protons in a magnetic field of 10Tesla) a) 106 rads b) 107 rads c) 1010 rads d) 109 rads e) 1011 rads

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

১৬ ৩০ েসিম লUা একিট (বাদযের) তােরর সবিন কQােRর মান ১০৩ হাজ তােরর টান িltন করা হেল তারিটেত

এখন ধাবমান তরের েবগ কত ( In a 30 cm long string of a musical instrument the fundamental note has

the frequency equal to 103Hz If now the tension in the string is double what is the speed of travelling waves on the string )

a) 300 ms b) 600ms c) 840ms d) 420ms e) 150ms

১৭ ইেলJেনর িবপরীত কনা হে$ পিজন যার ভর ইেলJেনর সমান অথা ৯১ x ১০-৩১ েকিজ িক7 চাজ সQণ

িবপরীত এরকম পিজন ও ইেলJেনর একিট েজাড়া ৈতরী করেত ননতম কতটক শিCর েয়াজন হেব ( The

antiparticle of electron is positron whose mass is the same as electrons ie 91 x 10-31 kg but the charge is opposite What is the minimum energy required to produce a electron-positron pair )

a) 22 MeV b) 50MeV c) 17MeV d) 085MeV e) 11 MeV

১৮ k1 ও k2 িং বেকর দিট িংেক এমনভােব লাগােনা হেলা যােত তােদর েতেকর একিট কের েখালা া থােক

েযিল ধের সংযC িংিটেক সািরত করা যায় সংযC িংিটর িং বেকর মান কত (Two springs with

spring constants k1 and k2 are attached together in a manner so that each of them has one end attached to the other and the remaining end is free for stretching under the action of external forces What is the equivalent spring constant for the joined spring )

a) k1 b) k2 c) k1 + k2 d) (k1

2 + k22 )12

e) k1 k2 (k1 + k2)

১৯ অসীম ৈদেঘর একিট েসাজা তাের I মােনর তিড় উপর েথেক িনেচর িদেক বাহমান যিদ q চােজর একিট কণােক

v েবেগ তােরর পব িদেক d দরে_ অবি5ত েকােনা িব হেত তােরর েকa তাক কের ভ-সমারােল িu করা হয়

উC চােজর উপর অনভত বেলর মান কত (An infinite wire carries a current I along the vertical direction If a

charge q is projected horizontally towards the center of the wire from a point which is east of the wire at a distance d away what is the force felt on the charge )

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b

a) micro0 qvI2πd b) 0 c) micro0 qvI4π d) micro0q

2I2πd e) micro0 qvI4πd

২০ উপেরর েf বল েকান িদক বরাবর কাজ করেব (What is the direction of the force exerted on the charge

in the above problem)

a) িনিদেক ( Downward )

b) উ িদেক ( Upward )

c) উরিদেক ( Towards North )

d) দিণিদেক ( Towards South )

e) পিমিদেক ( Towards West )

Barisal Answer Sheet Category C

Ques no Answer

1 c

2 d

3 e

4 b

5 a

6 c

7 d

8 e

9 d

10 a

11 b

12 c

13 a

14 c

15 d

16 c

17 e

18 e

19 a

20 b