physics (theory) -...
TRANSCRIPT
138
PHYSICS (Theory)
Time allowed : 3 hours Maximum Marks : 70
General Instructions:
(i) There are 26 questions in all. All questions are compulsory.
(ii) This question paper has five sections: Section A, Section B, Section C, Section
D and Section E.
(iii) Section A contains five questions of one mark each, Section B contains five
questions of two marks each, Section C contains twelve questions of three
marks each, Section D contains one value based question of four marks and
Section E contains three questions of five marks each.
(iv) There is no overall choice. However, an internal choice has been provided in
one question of two marks, one question of three marks and all the three
questions of five marks weightage. You have to attempt only one of the choices
in such questions.
(v) You may use the following values of physical constants wherever necessary:
c = 3 108 ms–1
h = 6.63 10–34 Js
e = 1.6 10–19 C
0 = 4 10–7 T mA–1
0 = 8.854 × 10–12 C2 N–1 m–2
04
1
= 9 109 N m2 C–2
me = 9.1 10–31 kg
139
QUESTION PAPER CODE 55/1/1/D
1. Define capacitative reactance. Write its S.I. units. 1
2. What is the electric flux through a cube of side 1 cm which encloses an electric
dipole? 1
3. A concave lens of refractive index 1.5 is immersed in a medium of refractive index
1.65. What is the nature of the lens ? 1
4. How are side bands produced ? 1
5. Graph showing the variation of current versus voltage for a material GaAs is shown
in the figure. Identify the region of
(i) negative resistance
(ii) where Ohm's law is obeyed. 1
mass of neutron = 1.675 × 10–27 kg
mass of proton = 1.673 × 10–27 kg
Avogadro's number = 6.023 × 1023 per gram mole
Boltzmann constant = 1.38 × 10–23 JK–1
140
Section-B
6. A proton and an a-particle have the same de-Broglie wavelength. Determine the
ratio of (i) their accelerating potentials and (ii) their speeds. 2
7. Show that the radius of the orbit in hydrogen atom varies as n2, where n is the
principal quantum number of the atom. 2
8. Distinguish between 'intrinsic' and 'extrinsic' semiconductors. 2
9. Use the mirror equation to show that an object placed between f and 2f of a concave
mirror produces a real image beyond 2f. 2
OR
Find an expression for intensity of transmitted light when a polaroid sheet is rotated
between two crossed polaroids. In which position of the polaroid sheet will the
transmitted intensity be maximum ?
10. Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone
bridge. 2
Section- C
11. Name the parts of the electromagnetic spectrum which is
(a) suitable for radar systems used in aircraft navigation.
(b) used to treat muscular strain.
(c) used as a diagnostic tool in medicine.
Write in brief, how these waves can be produced. 3
12. (i) A giant refracting telescope has an objective lens of focal length 15 m. If an
eye piece of focal length 1.0 cm is used, what is the angular magnification of
the telescope?
141
(ii) If this telescope is used to view the moon, what is the diameter of the image
of the moon formed by the objective lens? The diameter of the moon is
3.48 × 106 m and the radius of lunar orbit is 3.8 x 108 m. 3
13. Write Einstein's Photoelectric equation and mention which important features in
photoelectric effect can be explained with the help of this equation.
The maximum kinetic energy of the photoelectrons gets doubled when the wavelength
of light incident on the surface changes from 1 to
2. Derive the expressions for the
threshold wavelength 0 and work function for the metal surface. 3
14. In the study of Geiger-Marsdon experiment on scattering of particles by a thin
foil of gold, draw the trajectory of -particles in the Coulomb field of target
nucleus. Explain briefly how one gets the information on the size of the nucleus from
this study.
From the relation R = R0 A1/3, where R
0 is constant and A is the mass number of
the nucleus, show that nuclear matter density is independent of A. 3
OR
Distinguish between nuclear fission and fusion. Show how in both these processes
energy is released.
Calculate the energy release in MeV in the deuterium-tritium fusion reaction :
nHeHH 4
2
3
1
2
1
Using the data :
m( H2
1) = 2.014102 u
m( H3
1) = 3.016049 u
m( He4
2) = 4.002603 u
mn = 1.008665 u
l u = 931.5 MeV/c2
142
15. Draw a block diagram of a detector for AM signal and show, using necessary
processes and the waveforms, how the original message signal is detected from the
input AM wave. 3
16. A cell of emf 'E' and internal resistance 'r' is connected across a variable load
resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the
current I.
It is found that when R = 4 , the current is 1 A and when R is increased to 9 ,
the current reduces to 0.5 A. Find the values of the emf E and internal resistance r. 3
17. Two capacitors of unknown capacitances C1 and C
2 are connected first in series
and then in parallel across a battery of 100 V. If the energy stored in the two
combinations is 0.045 J and 0.25 J respectively, determine the value of C1 and C
2.
Also calculate the charge on each capacitor in parallel combination. 3
18. State the principle of working of a galvanometer.
A galvanometer of resistance G is converted into a voltmeter to measure upto V
volts by connecting a resistance R1 in series with the coil. If a resistance R
2 is connected
in series with it, then it can measure upto V/2 volts. Find the resistance, in terms of
R1 and R
2, required to be connected to convert it into a voltmeter that can read upto
2 V. Also find the resistance G of the galvanometer in terms of R1 and R
2. 3
19. With what considerations in view, a photodiode is fabricated ? State its working
with the help of a suitable diagram.
Eventhough the current in the forward bias is known to be more than in the reverse
bias, yet the photodiode works in reverse bias. What is the reason? 3
20. Draw a circuit diagram of a transistor amplifier in CE configuration.
Define the terms: (i) Input resistance and (ii) Current amplification factor. How are
these determined using typical input and output characteristics? 3
143
21. Answer the following questions:
(a) In a double slit experiment using light of wavelength 600 nm, the angular
width of the fringe formed on a distant screen is 0.1o. Find the spacing between
the two slits.
(b) Light of wavelength 5000 Å. propagating in air gets partly reflected from the
surface of water. How will the wavelengths and frequencies of the reflected
and refracted light be affected? 3
22. An inductor L of inductance XL is connected in series with a bulb B and an ac
source. How would brightness of the bulb change when (i) number of turns in the
inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a capacitor of
reactance XC = X
L is inserted in series in the circuit. Justify your answer in each case. 3
Section -D
23. A group of students while coming from the school noticed a box marked "Danger
H.T. 2200 V" at a substation in the main street. They did not understand the utility of
such a high voltage, while they argued, the supply was only 220 V.They asked their
teacher this question the next day. The teacher thought it to be an important question
and therefore explained to the whole class.
Answer the following questions:
(i) What device is used to bring the high voltage down to low voltage of a.c.
current and what is the principle of its working?
(ii) Is it possible to use this device for bringing down the high d.c. voltage to the
low voltage ? Explain.
(iii) Write the values displayed by the students and the teacher. 4
144
Section-E
24. (a) State Ampere's circuital law. Use this law to obtain the expression for the
magnetic field inside an air cored toroid of average radius 'r' having 'n' turns
per unit length and carrying a steady current I.
(b) An observer to the left of a solenoid of N turns each of cross section area 'A'
observes that a steady current I in it flows in the clockwise direction. Depict
the magnetic field lines due to the solenoid specifying its polarity and show
that it acts as a bar magnet of magnetic moment m = NIA. 5
OR
(a) Define mutual inductance and write its S.I. unit.
(b) Derive an expression for the mutual inductance of two long co-axial solenoids
of same length wound one over the other.
(c) In an experiment, two coils c1 and c
2 are placed close to each other. Find out
the expression for the emf induced in the coil c1 due to a change in the current
through the coil c2. 5
25. (a) Using Huygens's construction of secondary wavelets explain how a diffraction
pattern is obtained on a screen due to a narrow slit on which a monochromatic
beam of light is incident normally.
(b) Show that the angular width of the first diffraction fringe is half that of the
central fringe.
145
(c) Explain why the maxima at = a
λ
2
1 n
become weaker and weaker with
increasing n. 5
OR
(a) A point object 'O' is kept in a medium of refractive index n1 in front of a
convex spherical surface of radius of curvature R which separates the second
medium of refractive index n2 from the first one, as shown in the figure.
Draw the ray diagram showing the image formation and deduce the relationship
between the object distance and the image distance in terms of n1, n
2 and R.
(b) When the image formed above acts as a virtual object for concave spherical,
surface separating the medium n2 from n
1 (n
2 > n
1), draw this ray diagram and
write the similar (similar to (a)) relation. Hence obtain the expression for the
lens maker's formula. 5
26. (a) An electric dipole of dipole moment p
consists of point charges +q and -q
separated by a distance 2a apart. Deduce the expression for the electric field
E
due to the dipole at a distance x from the centre of the dipole on its axial
line in terms of the dipole moment p
. Hence show that in the limit x >> a,
p2E / (40x3).
146
(b) Given the electric field in the region
i2E x , find the net electric flux through
the cube and the charge enclosed by it. 5
OR
(a) Explain, using suitable diagrams, the difference in the behaviour of a (i) conductor
and (ii) dielectric in the presence of an external electric field. Define the terms
polarization of a dielectric and write its relation with susceptibility.
(b) A thin metallic spherical shell of radius R carries a charge Q on its surface. A
point charge 2
Q is placed at its centre C and an other charge +2Q is placed
outside the shell at a distance x from the centre as shown in the figure. Find
(i) the force on the charge at the centre of shell and at the point A and (ii) the
electric flux through the shell.
A
2Qx
176
QUESTION PAPER CODE 55(B)
SECTION A
1. Where on the surface of Earth, is the vertical component of Earth's magnetic field
zero? 1
2. Define the term 'rms' value of the current. How is it related to the peak value? 1
3. Write the expression for the de Broglie wavelength associated with an electron
accelerated through a potential 'V'. 1
4. An electron does not suffer any deflection while passing through a region of uniform
magnetic field. What is the direction of the magnetic field ? 1
5. Why is convex mirror used as a side view mirror in a car? 1
SECTION B
6. A point charge causes an electric flux of – 1 × 103 Nm2/C to pass through a
spherical Gaussian surface of 10·0 cm radius centred on the charge.
(a) What is the value of the point charge?
(b) If the radius of the Gaussian surface were doubled, how much flux would
pass through the surface? 2
7. State Lenz's law. Show that it is a consequence of the principle of conservation of
energy. 2
8. (i) What is the power of the lens whose focal length is 0·25 m?
(ii) The radii of curvature of the faces of a double convex lens are 20 cm and
25 cm. Its focal length is 20 cm. Calculate the refractive index of the material. 2
9. Define electrical resistivity of a given material. Why does resistivity of a metal
increase with the increase in temperature whereas in the case of a semiconductor
it decreases? 2
177
10. Write the functions of (i) transmitter and (ii) transducer in the context of communi-
cation system. 2
OR
Write two factors justifying the need of modulation for transmission of a signal. 2
SECTION C
11. (a) Describe briefly how an oscillating charge can produce an electromagnetic
wave propagating through space.
(b) Which part of the. electromagnetic spectrum is used in satellite communica-
tion ? 3
12. (a) In an unbiased p-n junction, why do holes from p-region diffuse to n -region?
(b) What is the effect of forward biasing on (i) barrier potential and (ii) depletion
layer, in a p-n junction diode? 3
13. Explain the terms (i) threshold frequency and (ii) stopping potential, using Einstein's
photoelectric equation.
State clearly one observed feature in photoelectric effect which cannot be explained
by wave nature of light. 3
14. Write two characteristic properties of nuclear force. How does one explain the
release of energy in the processes of nuclear fusion and nuclear fission ? 3
15. State the underlying principle of a cyclotron. Obtain the expression for cyclotron
frequency and explain how it is used to accelerate the charged particles. 3
16. Define the term 'linearly polarised light'. How does an unpolarised light get linearly
polarised when passed through a polaroid ? When does the intensity of transmitted
178
light become maximum when a polaroid sheet is rotated between two crossed
polaroids ? 3
17. Explain briefly how an n-p-n transistor is fabricated. Define the terms (i) input
resistance and (ii) current amplification factor (B) of a transistor, used in its CE
configuration. 3
OR
State the underlying principle of a full wave rectifier. Explain how it works. 3
18. (a) How is the electric field due to a charged parallel plate capacitor affected
when a dielectric slab is inserted between the plates fully occupying the
intervening space?
(b) A slab of material of dielectric constant K has the same area as the plates of a
parallel plate capacitor but has the thickness d/2, where'd' is the separation
between the plates. Find the expression for the capacitance when the slab is
inserted between the plates. 3
19. Explain the working of an astronomical telescope. The magnifying power of a
telescope in its normal adjustment is 20. If the length of the telescope is 105 cm in
this adjustment, find the focal lengths of both the lenses. 3
20. State Ampere's circuital law. Using this law, deduce the expression for the magnetic
field due to a thin straight infinitely long current carrying wire at a distance ' r' from
it. 3
21. The ground state energy of hydrogen atom is -13·6 eV. If an electron makes a
transition from an energy level - 0·85 eV to - 3·4 eV, calculate the wavelength of the
spectral line emitted. To which series of hydrogen spectrum does this wavelength
belong? 3
22. Consider a large spherical shell of radius 'R' on which a charge 'Q' is placed. If we
place a small sphere of radius ' r ' carrying a charge 'q' at the centre of the large
179
sphere, find out the expressions for the total potential on the surface of the outer
shell and inner sphere. Which one would be at a higher potential and why? 3
SECTION D
23. Anuj has the habit of talking on his mobile phone for a long span of time. One day,
when he was absent from the school, he contacted his friend and asked about the
homework. He then asked his friend how to solve these problems. His sister, Meena,
kept on watching him. She finally suggested to him that if he had to talk for such a
long time, it would be better if he used the land line. She explained how a prolonged
exposure and use of a mobile phone. over a long time could be harmful. Anuj got
convinced and accepted his sister's advice.
Based on the above paragraph, answer the following questions:
(a) What, according to you, are the values displayed by Meena?
(b) In what way could the use of mobile phone for a long time be harmful?
(c) Find out the range upto which electromagnetic waves can be transmitted
from an antenna of height 320 m. (Given: Radius of Earth = 6·4 × 106 m) 4
SECTION E
24. Explain briefly the principle and working of the device used for comparing the emfs
of two cells. Define the potential gradient and write its S.I. unit. How can the current
sensitivity of such a device be increased ? In what way is this method of comparing
the emfs of two cells different from the one using voltmeter? 5
OR
(a) Use Kirchhoff's rules to obtain the balance condition in terms of the values of
the four resistors in a Wheatstone bridge so as to obtain null deflection in the
galvanometer.
180
(b) Explain how the balance condition in Wheatstone bridge is used in meter
bridge to determine the value of unknown resistance. Under what condition is
the error in determining the unknown resistance minimized ? 5
25. (a) Derive the condition for resonance in a series LCR circuit connected to an
a.c. source of variable frequency.
(b) Define the following terms :
(i) Q- factor
(ii) Power factor
(iii) Wattless current 5
OR
(a) Explain the working principle of a step-up transformer. Deduce the expression
for the secondary to primary voltage in terms of the number of turns in the two
coils. In an ideal transformer, how is this ratio related to the currents in the
two coils?
(b) How are the transformers used in large scale transmission and distribution of
electrical energy over long distances? 5
26. (a) A parallel beam of monochromatic light falls normally on a narrow slit and the
light coming out of the slit is obtained on a screen kept parallel to the plane of
the slit. What kind of pattern do we observe on the screen and why ? How
does the (i) angular width and (ii) linear width of the principal maximum in this
pattern change when the source is moved parallel to itself away from the slit
plane?
(b) State two points of difference between this pattern and the interference pattern
observed in Young's double slit experiment. 5
181
OR
(a) What is meant by coherent sources. ? 'Why are they necessary for observing
a sustained interference pattern?
(b) Show that the superposition of the waves originating from two coherent sources
S1 and S
2 described by y
1 = a cos t and y
2 = a cos (t + ) at a point,
produces a resultant intensity
I = 4 a2 cos2 /2
Hence write the conditions for the appearance of dark and bright fringes. 5