simple harmonic motion, a = – ω2x velocity of particle in s.h.m., v = v ... kinetic energy e k 2...

This document consists of 21 printed pages and 3 blank pages.

DC (LEO/CGW) 15337/4© UCLES 2010 [Turn over

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSGeneral Certificate of Education Advanced Level

*7303645500*

PHYSICS 9702/41

Paper 4 A2 Structured Questions May/June 2010

1 hour 45 minutes

Candidates answer on the Question Paper.

No Additional Materials are required.

READ THESE INSTRUCTIONS FIRST

Write your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use a soft pencil for any diagrams, graphs or rough working.Do not use staples, paper clips, highlighters, glue or correction fluid.DO NOT WRITE IN ANY BARCODES.

Answer all questions.You may lose marks if you do not show your working or if you do not use appropriate units.

At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.

For Examiner’s Use

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Data

speed of light in free space, c = 3.00 × 108 m s–1

permeability of free space, μ0 = 4π × 10–7 H m–1

permittivity of free space, ε0 = 8.85 × 10–12 F m–1

elementary charge, e = 1.60 × 10–19 C

the Planck constant, h = 6.63 × 10–34 J s

unified atomic mass constant, u = 1.66 × 10–27 kg

rest mass of electron, me = 9.11 × 10–31 kg

rest mass of proton, mp = 1.67 × 10–27 kg

molar gas constant, R = 8.31 J K–1 mol–1

the Avogadro constant, NA = 6.02 × 1023 mol–1

the Boltzmann constant, k = 1.38 × 10–23 J K–1

gravitational constant, G = 6.67 × 10–11 N m2 kg–2

acceleration of free fall, g = 9.81 m s–2

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Formulae

uniformly accelerated motion, s = ut + �� at 2

v2 = u2 + 2as

work done on/by a gas, W = p�V

gravitational potential, φ = – Gmr

hydrostatic pressure, p = ρgh

pressure of an ideal gas, p = �� NmV

<c2>

simple harmonic motion, a = – ω2x

velocity of particle in s.h.m., v = v0 cos ωt

v = ± ω √⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ (x02 – x2)

electric potential, V = Q4πε0r

capacitors in series, 1/C = 1/C1 + 1/C2 + . . .

capacitors in parallel, C = C1 + C2 + . . .

energy of charged capacitor, W = �� QV

resistors in series, R = R1 + R2 + . . .

resistors in parallel, 1/R = 1/R1 + 1/R2 + . . .

alternating current/voltage, x = x0 sin ωt

radioactive decay, x = x0 exp(– λt )

decay constant, λ = 0.693

t ��

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Section A

Answer all the questions in the spaces provided.

1 (a) Define the radian.

..........................................................................................................................................

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...................................................................................................................................... [2]

(b) A stone of weight 3.0 N is fixed, using glue, to one end P of a rigid rod CP, as shown in Fig. 1.1.

85 cm

C

P

ω

glue

stone,weight 3.0 N

Fig. 1.1

The rod is rotated about end C so that the stone moves in a vertical circle of radius 85 cm.

The angular speed ω of the rod and stone is gradually increased from zero until the glue snaps. The glue fixing the stone snaps when the tension in it is 18 N.

For the position of the stone at which the glue snaps,

(i) on the dotted circle of Fig. 1.1, mark with the letter S the position of the stone, [1]

(ii) calculate the angular speed ω of the stone.

angular speed = ................................... rad s–1 [4]

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2 (a) Some gas, initially at a temperature of 27.2 °C, is heated so that its temperature rises to 38.8 °C.

Calculate, in kelvin, to an appropriate number of decimal places,

(i) the initial temperature of the gas,

initial temperature = ............................................. K [2]

(ii) the rise in temperature.

rise in temperature = ............................................ K [1]

(b) The pressure p of an ideal gas is given by the expression

p = 13ρ�c 2�

where ρ is the density of the gas.

(i) State the meaning of the symbol �c 2�.

..................................................................................................................................

.............................................................................................................................. [1]

(ii) Use the expression to show that the mean kinetic energy <EK> of the atoms of an ideal gas is given by the expression

<EK> = 32 kT.

Explain any symbols that you use.

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(c) Helium-4 may be assumed to behave as an ideal gas. A cylinder has a constant volume of 7.8 × 103 cm3 and contains helium-4 gas at a

pressure of 2.1 × 107 Pa and at a temperature of 290 K.

Calculate, for the helium gas,

(i) the amount of gas,

amount = ......................................... mol [2]

(ii) the mean kinetic energy of the atoms,

mean kinetic energy = .............................................. J [2]

(iii) the total internal energy.

internal energy = .............................................. J [3]

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3 (a) State what is meant by

(i) oscillations,

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(ii) free oscillations,

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.............................................................................................................................. [1]

(iii) simple harmonic motion.

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.............................................................................................................................. [2]

(b) Two inclined planes RA and LA each have the same constant gradient. They meet at their lower edges, as shown in Fig. 3.1.

L R

ball

A

Fig. 3.1

A small ball moves from rest down plane RA and then rises up plane LA. It then moves down plane LA and rises up plane RA to its original height. The motion repeats itself.

State and explain whether the motion of the ball is simple harmonic.

..........................................................................................................................................

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...................................................................................................................................... [2]

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4 (a) Explain what is meant by the potential energy of a body.

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(b) Two deuterium ( 21 H) nuclei each have initial kinetic energy EK and are initially separated

by a large distance. The nuclei may be considered to be spheres of diameter 3.8 × 10–15 m with their masses

and charges concentrated at their centres. The nuclei move from their initial positions to their final position of just touching, as

illustrated in Fig. 4.1.

Hinitially

kinetic energy EK

21 H

H

3.8 × 10–15 m

at rest

finally H

kinetic energy EK

21

21

21

Fig. 4.1

(i) For the two nuclei approaching each other, calculate the total change in

1. gravitational potential energy,

energy = ............................................ J [3]

2. electric potential energy.

energy = ............................................ J [3]

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(ii) Use your answers in (i) to show that the initial kinetic energy EK of each nucleus is 0.19 MeV.

[2]

(iii) The two nuclei may rebound from each other. Suggest one other effect that could happen to the two nuclei if the initial kinetic energy of each nucleus is greater than that calculated in (ii).

..................................................................................................................................

.............................................................................................................................. [1]

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5 (a) A constant current is maintained in a long straight vertical wire. A Hall probe is positioned a distance r from the centre of the wire, as shown in Fig. 5.1.

X Y

Hall probe

terminals toHall probe circuitryand voltmeter

current-carryingwire

r

Fig. 5.1

(i) Explain why, when the Hall probe is rotated about the horizontal axis XY, the Hall voltage varies between a maximum positive value and a maximum negative value.

..................................................................................................................................

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.............................................................................................................................. [2]

(ii) The maximum Hall voltage VH is measured at different distances r. Data for VH and the corresponding values of r are shown in Fig. 5.2.

VH / V r / cm

0.2900.1900.1400.0970.0730.060

1.01.52.03.04.05.0

Fig. 5.2

It is thought that VH and r are related by an expression of the form

VH = kr

where k is a constant.

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1. Without drawing a graph, use data from Fig. 5.2 to suggest whether the expression is valid.

[2]

2. A graph showing the variation with 1r

of VH is plotted.

State the features of the graph that suggest that the expression is valid.

..............................................................................................................................

.......................................................................................................................... [1]

(b) The Hall probe in (a) is now replaced with a small coil of wire connected to a sensitive voltmeter. The coil is arranged so that its plane is normal to the magnetic field of the wire.

(i) State Faraday’s law of electromagnetic induction and hence explain why the voltmeter indicates a zero reading.

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.............................................................................................................................. [3]

(ii) State three different ways in which an e.m.f. may be induced in the coil.

1. ..............................................................................................................................

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2. ..............................................................................................................................

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3. ..............................................................................................................................

.................................................................................................................................. [3]

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6 A student is asked to design a circuit by which a direct voltage of peak value 9.0 V is obtained from a 240 V alternating supply.

The student uses a transformer that may be considered to be ideal and a bridge rectifier incorporating four ideal diodes.

The partially completed circuit diagram is shown in Fig. 6.1.

240 V

load

+

–

Fig. 6.1

(a) On Fig. 6.1, draw symbols for the four diodes so as to produce the polarity across the load as shown on the diagram. [2]

(b) Calculate the ratio

number of turns on the secondary coilnumber of turns on the primary coil

.

ratio = ................................................ [3]

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7 Negatively-charged particles are moving through a vacuum in a parallel beam. The particles have speed v.

The particles enter a region of uniform magnetic field of flux density 930 μT. Initially, the particles are travelling at right-angles to the magnetic field. The path of a single particle is shown in Fig. 7.1.

negatively-charged

particles, speed v

uniform magnetic field,flux density 930 μT

arc of radius 7.9 cm

Fig. 7.1

The negatively-charged particles follow a curved path of radius 7.9 cm in the magnetic field.

A uniform electric field is then applied in the same region as the magnetic field. For an electric field strength of 12 kV m–1, the particles are undeviated as they pass through the region of the fields.

(a) On Fig. 7.1, mark with an arrow the direction of the electric field. [1]

(b) Calculate, for the negatively-charged particles,

(i) the speed v,

v = ....................................... m s–1 [3]

(ii) the ratio chargemass

.

ratio = .................................... C kg–1 [3]

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8 A π0 meson is a sub-atomic particle. A stationary π0 meson, which has mass 2.4 × 10–28 kg, decays to form two γ-ray photons. The nuclear equation for this decay is

π0 γ + γ.

(a) Explain why the two γ-ray photons have the same energy.

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [2]

(b) Determine, for each γ-ray photon,

(i) the energy, in joule,

energy = .............................................. J [2]

(ii) the wavelength,

wavelength = ............................................ m [2]

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(iii) the momentum.

momentum = ........................................... N s [2]

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Section B


9 The circuit diagram of Fig. 9.1 is an amplifier circuit incorporating an operational amplifier (op-amp).

1.5 V

1.0 kΩ

4.2 kΩ

+9 V

–9 V

+

–

+

–V

Fig. 9.1

(a) (i) On Fig. 9.1, mark, with the letter X, the virtual earth. [1]

(ii) Explain what is meant by a virtual earth.

..................................................................................................................................

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [3]

(b) In bright sunlight, the light-dependent resistor (LDR) has resistance 200 Ω.

(i) Calculate, for the LDR in bright sunlight, the voltmeter reading.

reading = ............................................ V [3]

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(ii) The sunlight incident on the LDR becomes less bright. State and explain the effect on the voltmeter reading of this decrease in

brightness.

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.............................................................................................................................. [3]

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10 (a) Briefly explain the principles of CT scanning.

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(b) A simple section through a body consists of four voxels, as illustrated in Fig. 10.1.

section

directionsof viewing

Fig. 10.1

An X-ray image of the section is obtained by viewing along each of the directions shown in Fig. 10.1.

The detector readings for each direction of viewing are summed to give the pattern of readings shown in Fig. 10.2.

25

34

22

31

Fig. 10.2

For any one direction, the total of the detector readings is 16.

(i) For the pattern of readings of Fig. 10.2, state the magnitude of the background reading.

background reading = ................................................ [1]

(ii) On Fig. 10.1, mark the pattern of pixels for the four-voxel section. [2]

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11 Many radio stations now broadcast on FM rather than on AM. In general, FM is broadcast at much higher frequencies than AM.

(a) Explain what is meant by FM (frequency modulation).

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...................................................................................................................................... [2]

(b) State two advantages and two disadvantages of FM transmissions when compared with AM transmissions.

advantages of FM transmissions

1. .....................................................................................................................................

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2. .....................................................................................................................................

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disadvantages of FM transmissions

1. .....................................................................................................................................

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2. .....................................................................................................................................

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12 A ground station on Earth transmits a signal of frequency 14 GHz and power 18 kW towards a communications satellite orbiting the Earth, as illustrated in Fig. 12.1.

Earth

ground station,signal power18 kW

satellite

signal frequency

14 GHz

Fig. 12.1

The loss in signal power between the ground station and the satellite is 190 dB.

(a) Calculate the power of the signal received by the satellite.

power = .......................................... W [3]

(b) The signal received by the satellite is amplified and transmitted back to Earth.

(i) Suggest a frequency for the signal that is sent back to Earth.

frequency = ...................................... GHz [1]

(ii) Give a reason for your answer in (i).

..................................................................................................................................

.............................................................................................................................. [1]

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DC (LEO/DJ) 17381/5© UCLES 2010 [Turn over






*8631935288*

PHYSICS 9702/42


1 hour 45 minutes




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Data














3


Formulae

uniformly accelerated motion, s = ut + 12at 2

v2 = u2 + 2as



hydrostatic pressure, p = �gh

pressure of an ideal gas, p = 13

NmV

<c 2>

simple harmonic motion, a = – �2x

velocity of particle in s.h.m., v = v0 cos �t

v = ± ω (x02 – x 2)

electric potential, V = Q4π�0r



energy of charged capacitor, W = 12 QV




radioactive decay, x = x0 exp(– λt)

decay constant, λ = 0.693t 1

2

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ForExaminer’s

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Section A


1 (a) Define gravitational potential at a point.

..........................................................................................................................................

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.................................................................................................................................... [2]

(b) The Earth may be considered to be an isolated sphere of radius R with its mass concentrated at its centre.

The variation of the gravitational potential φ with distance x from the centre of the Earth is shown in Fig. 1.1.

0

–2.0

/ 107 J kg–1

–4.0

–6.0

–8.0

0 R 2R

distance x

3R 4R 5R

Fig. 1.1

The radius R of the Earth is 6.4 × 106 m.

(i) By considering the gravitational potential at the Earth’s surface, determine a value for the mass of the Earth.

mass = ......................................... kg [3]

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(ii) A meteorite is at rest at infinity. The meteorite travels from infinity towards the Earth.

Calculate the speed of the meteorite when it is at a distance of 2R above the Earth’s surface. Explain your working.

speed = ..................................... m s–1 [4]

(iii) In practice, the Earth is not an isolated sphere because it is orbited by the Moon, as illustrated in Fig. 1.2.

Earth

Moon

initial pathof meteorite

Fig. 1.2 (not to scale)

The initial path of the meteorite is also shown.

Suggest two changes to the motion of the meteorite caused by the Moon.

1. ..............................................................................................................................

..................................................................................................................................

2. ..............................................................................................................................

..................................................................................................................................[2]

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2 A long strip of springy steel is clamped at one end so that the strip is vertical. A mass of 65 g is attached to the free end of the strip, as shown in Fig. 2.1.

mass65 g

clamp

springysteel

Fig. 2.1

The mass is pulled to one side and then released. The variation with time t of the horizontal displacement of the mass is shown in Fig. 2.2.

2

1

displacement/ cm

0

–1

–2

0.10.10.10 0.2 0.3 0.4 0.5 0.6 0.7t / s

Fig. 2.2

The mass undergoes damped simple harmonic motion.

(a) (i) Explain what is meant by damping.

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............................................................................................................................ [2]

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(ii) Suggest, with a reason, whether the damping is light, critical or heavy.

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(b) (i) Use Fig. 2.2 to determine the frequency of vibration of the mass.

frequency = ......................................... Hz [1]

(ii) Hence show that the initial energy stored in the steel strip before the mass is released is approximately 3.2 mJ.

[2]

(c) After eight complete oscillations of the mass, the amplitude of vibration is reduced from 1.5 cm to 1.1 cm. State and explain whether, after a further eight complete oscillations, the amplitude will be 0.7 cm.

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3 (a) The resistance of a thermistor at 0 °C is 3840 Ω. At 100 °C the resistance is 190 Ω. When the thermistor is placed in water at a particular constant temperature, its resistance

is 2300 Ω.

(i) Assuming that the resistance of the thermistor varies linearly with temperature, calculate the temperature of the water.

temperature = ......................................... °C [2]

(ii) The temperature of the water, as measured on the thermodynamic scale of temperature, is 286 K.

By reference to what is meant by the thermodynamic scale of temperature, comment on your answer in (i).

..................................................................................................................................

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............................................................................................................................ [3]

(b) A polystyrene cup contains a mass of 95 g of water at 28 °C.

A cube of ice of mass 12 g is put into the water. Initially, the ice is at 0 °C. The water, of specific heat capacity 4.2 × 103 J kg–1 K–1, is stirred until all the ice melts.

Assuming that the cup has negligible mass and that there is no heat exchange with the atmosphere, calculate the final temperature of the water.

The specific latent heat of fusion of ice is 3.3 × 105 J kg–1.

temperature = ......................................... °C [4]

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4 Two point charges A and B each have a charge of + 6.4 × 10–19 C. They are separated in a vacuum by a distance of 12.0 μm, as shown in Fig. 4.1.

12.0 μm

A P Q B

3.0 μm

+6.4 × 10–19 C +6.4 × 10–19 C

3.0 μm

Fig. 4.1

Points P and Q are situated on the line AB. Point P is 3.0 μm from charge A and point Q is 3.0 μm from charge B.

(a) Calculate the force of repulsion between the charges A and B.

force = .......................................... N [3]

(b) Explain why, without any calculation, when a small test charge is moved from point P to point Q, the net work done is zero.

..........................................................................................................................................

..........................................................................................................................................

.................................................................................................................................... [2]

(c) Calculate the work done by an electron in moving from the midpoint of line AB to point P.

work done = ........................................... J [4]

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5 (a) State two functions of capacitors in electrical circuits.

1. .....................................................................................................................................

2. ..................................................................................................................................... [2]

(b) Three capacitors, each marked ‘30 μF, 6 V max’, are arranged as shown in Fig. 5.1.

A B

Fig. 5.1

Determine, for the arrangement shown in Fig. 5.1,

(i) the total capacitance,

capacitance = ......................................... μF [2]

(ii) the maximum potential difference that can safely be applied between points A and B.

potential difference = ........................................... V [2]

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(c) A capacitor of capacitance 4700 μF is charged to a potential difference of 18 V. It is then partially discharged through a resistor. The potential difference is reduced to 12 V.

Calculate the energy dissipated in the resistor during the discharge.

energy = ........................................... J [3]

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6 (a) A uniform magnetic field has constant flux density B. A straight wire of fixed length carries a current I at an angle θ to the magnetic field, as shown in Fig. 6.1.

magnetic fieldflux density B


I

Fig. 6.1

(i) The current I in the wire is changed, keeping the angle θ constant. On Fig. 6.2, sketch a graph to show the variation with current I of the force F on the

wire.

0

F

I0

Fig. 6.2 [2]

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(ii) The angle θ between the wire and the magnetic field is now varied. The current I is kept constant.

On Fig. 6.3, sketch a graph to show the variation with angle θ of the force F on the wire.

F

00

30 60 90

/ °

Fig. 6.3 [3]

(b) A uniform magnetic field is directed at right-angles to the rectangular surface PQRS of a slice of a conducting material, as shown in Fig. 6.4.

Q R

direction ofmovementof electrons

uniform magnetic field

SP

Fig. 6.4

Electrons, moving towards the side SR, enter the slice of conducting material. The electrons enter the slice at right-angles to side SR.

(i) Explain why, initially, the electrons do not travel in straight lines across the slice from side SR to side PQ.

..................................................................................................................................

..................................................................................................................................

............................................................................................................................ [2]

(ii) Explain to which side, PS or QR, the electrons tend to move.

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7 (a) Explain what is meant by the root-mean-square (r.m.s.) value of an alternating voltage.

..........................................................................................................................................

..........................................................................................................................................

.................................................................................................................................... [2]

(b) An alternating voltage V is represented by the equation

V = 220 sin(120πt),

where V is measured in volts and t is in seconds.

For this alternating voltage, determine

(i) the peak voltage,

peak voltage = ........................................... V [1]

(ii) the r.m.s. voltage,

r.m.s. voltage = ........................................... V [1]

(iii) the frequency.

frequency = ......................................... Hz [1]

(c) The alternating voltage in (b) is applied across a resistor such that the mean power output from the resistor is 1.5 kW.

Calculate the resistance of the resistor.

resistance = .......................................... Ω [2]


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8 Americium-241 is an artificially produced radioactive element that emits α-particles. A sample of americium-241 of mass 5.1 μg is found to have an activity of 5.9 × 105 Bq.

(a) Determine, for this sample of americium-241,

(i) the number of nuclei,

number = ............................................... [2]

(ii) the decay constant,

decay constant = ........................................ s–1 [2]

(iii) the half-life, in years.

half-life = .................................... years [2]

(b) Another radioactive element has a half-life of approximately 4 hours. Suggest why measurement of the mass and activity of a sample of this element is not

appropriate for the determination of its half-life.

..........................................................................................................................................

.................................................................................................................................... [1]

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Section B


9 (a) Negative feedback may be used in amplifier circuits. State

(i) what is meant by negative feedback,

..................................................................................................................................

..................................................................................................................................

............................................................................................................................ [2]

(ii) two effects of negative feedback on an amplifier incorporating an operational amplifier (op-amp).

1. ...............................................................................................................................

..................................................................................................................................

2. ...............................................................................................................................

.................................................................................................................................. [2]

(b) Fig. 9.1 is a circuit for an amplifier that is used with a microphone.

microphone

P

120 kΩ

R

V OUT

Fig. 9.1

The output potential difference VOUT is 4.4 V when the potential at point P is 62 mV.

Determine

(i) the gain of the amplifier,

gain = ............................................... [1]

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(ii) the resistance of the resistor R.

resistance = .......................................... Ω [2]

(c) The maximum potential produced by the microphone at point P on Fig. 9.1 is 95 mV. The power supply for the operational amplifier may be either +/– 5 V or +/– 9 V.

State which power supply should be used. Justify your answer quantitatively.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

.................................................................................................................................... [3]

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10 (a) State the name of an electrical sensing device that will respond to changes in

(i) length,

............................................................................................................................ [1]

(ii) pressure.

............................................................................................................................ [1]

(b) A relay is sometimes used as the output of a sensing circuit.

The output of a particular sensing circuit is either + 2 V or – 2 V.

On Fig. 10.1, draw symbols for a relay and any other necessary component so that the external circuit is switched on only when the output from the sensing circuit is + 2 V.

terminalsof externalcircuit

output fromsensing circuit

+2 V or –2 V

Fig. 10.1 [4]

19

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[Turn over

11 Explain the main principles behind the generation of ultrasound to obtain diagnostic information about internal body structures.

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

........................................................................................................................................... [6]

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12 A telephone link between two towns is to be provided using an optic fibre. The length of the optic fibre between the two towns is 75 km.

(a) State two changes that occur in a signal as it is transmitted along an optic fibre.

1. ......................................................................................................................................

..........................................................................................................................................

2. ......................................................................................................................................

.......................................................................................................................................... [2]

(b) The optic fibre has an attenuation per unit length of 1.6 dB km–1. The minimum permissible signal-to-noise power ratio in the fibre is 25 dB. The average noise power in the optic fibre is 6.1 × 10–19 W.

(i) Suggest one reason why power ratios are expressed in dB.

..................................................................................................................................

............................................................................................................................ [1]

(ii) The signal input power to the optic fibre is designed to be 6.5 mW. Determine whether repeater amplifiers are necessary in the optic fibre between the

two towns.

[5]




DC (SM/DJ) 28740© UCLES 2010 [Turn over






*8470198490*

PHYSICS 9702/43


1 hour 45 minutes




1

2

3

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5

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Data














3


Formulae

uniformly accelerated motion, s = ut + 12at 2

v2 = u2 + 2as



hydrostatic pressure, p = �gh


NmV

<c 2>

simple harmonic motion, a = – �2x

velocity of particle in s.h.m., v = v0 cos �t

v = ± ω (x02 – x 2)

electric potential, V = Q4π�0r







radioactive decay, x = x0 exp(– λt)

decay constant, λ = 0.693t 1

2

4

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Section A


1 (a) Define gravitational potential at a point.

..........................................................................................................................................

..........................................................................................................................................

.................................................................................................................................... [2]

(b) The Earth may be considered to be an isolated sphere of radius R with its mass concentrated at its centre.

The variation of the gravitational potential φ with distance x from the centre of the Earth is shown in Fig. 1.1.

0

–2.0

/ 107 J kg–1

–4.0

–6.0

–8.0

0 R 2R

distance x

3R 4R 5R

Fig. 1.1

The radius R of the Earth is 6.4 × 106 m.

(i) By considering the gravitational potential at the Earth’s surface, determine a value for the mass of the Earth.

mass = ......................................... kg [3]

4

5


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(ii) A meteorite is at rest at infinity. The meteorite travels from infinity towards the Earth.

Calculate the speed of the meteorite when it is at a distance of 2R above the Earth’s surface. Explain your working.

speed = ..................................... m s–1 [4]

(iii) In practice, the Earth is not an isolated sphere because it is orbited by the Moon, as illustrated in Fig. 1.2.

Earth

Moon

initial pathof meteorite


The initial path of the meteorite is also shown.

Suggest two changes to the motion of the meteorite caused by the Moon.

1. ..............................................................................................................................

..................................................................................................................................

2. ..............................................................................................................................

..................................................................................................................................[2]

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2 A long strip of springy steel is clamped at one end so that the strip is vertical. A mass of 65 g is attached to the free end of the strip, as shown in Fig. 2.1.

mass65 g

clamp

springysteel

Fig. 2.1

The mass is pulled to one side and then released. The variation with time t of the horizontal displacement of the mass is shown in Fig. 2.2.

2

1

displacement/ cm

0

–1

–2

0.10.10.10 0.2 0.3 0.4 0.5 0.6 0.7t / s

Fig. 2.2

The mass undergoes damped simple harmonic motion.

(a) (i) Explain what is meant by damping.

..................................................................................................................................

..................................................................................................................................

............................................................................................................................ [2]

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(ii) Suggest, with a reason, whether the damping is light, critical or heavy.

..................................................................................................................................

..................................................................................................................................

............................................................................................................................ [2]

(b) (i) Use Fig. 2.2 to determine the frequency of vibration of the mass.

frequency = ......................................... Hz [1]

(ii) Hence show that the initial energy stored in the steel strip before the mass is released is approximately 3.2 mJ.

[2]

(c) After eight complete oscillations of the mass, the amplitude of vibration is reduced from 1.5 cm to 1.1 cm. State and explain whether, after a further eight complete oscillations, the amplitude will be 0.7 cm.

..........................................................................................................................................

..........................................................................................................................................

.................................................................................................................................... [2]

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3 (a) The resistance of a thermistor at 0 °C is 3840 Ω. At 100 °C the resistance is 190 Ω. When the thermistor is placed in water at a particular constant temperature, its resistance

is 2300 Ω.

(i) Assuming that the resistance of the thermistor varies linearly with temperature, calculate the temperature of the water.

temperature = ......................................... °C [2]

(ii) The temperature of the water, as measured on the thermodynamic scale of temperature, is 286 K.

By reference to what is meant by the thermodynamic scale of temperature, comment on your answer in (i).

..................................................................................................................................

..................................................................................................................................

..................................................................................................................................

............................................................................................................................ [3]

(b) A polystyrene cup contains a mass of 95 g of water at 28 °C.

A cube of ice of mass 12 g is put into the water. Initially, the ice is at 0 °C. The water, of specific heat capacity 4.2 × 103 J kg–1 K–1, is stirred until all the ice melts.

Assuming that the cup has negligible mass and that there is no heat exchange with the atmosphere, calculate the final temperature of the water.

The specific latent heat of fusion of ice is 3.3 × 105 J kg–1.

temperature = ......................................... °C [4]

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4 Two point charges A and B each have a charge of + 6.4 × 10–19 C. They are separated in a vacuum by a distance of 12.0 μm, as shown in Fig. 4.1.

12.0 μm

A P Q B

3.0 μm

+6.4 × 10–19 C +6.4 × 10–19 C

3.0 μm

Fig. 4.1

Points P and Q are situated on the line AB. Point P is 3.0 μm from charge A and point Q is 3.0 μm from charge B.

(a) Calculate the force of repulsion between the charges A and B.

force = .......................................... N [3]

(b) Explain why, without any calculation, when a small test charge is moved from point P to point Q, the net work done is zero.

..........................................................................................................................................

..........................................................................................................................................

.................................................................................................................................... [2]

(c) Calculate the work done by an electron in moving from the midpoint of line AB to point P.

work done = ........................................... J [4]

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5 (a) State two functions of capacitors in electrical circuits.

1. .....................................................................................................................................

2. ..................................................................................................................................... [2]

(b) Three capacitors, each marked ‘30 μF, 6 V max’, are arranged as shown in Fig. 5.1.

A B

Fig. 5.1

Determine, for the arrangement shown in Fig. 5.1,

(i) the total capacitance,

capacitance = ......................................... μF [2]

(ii) the maximum potential difference that can safely be applied between points A and B.

potential difference = ........................................... V [2]

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(c) A capacitor of capacitance 4700 μF is charged to a potential difference of 18 V. It is then partially discharged through a resistor. The potential difference is reduced to 12 V.

Calculate the energy dissipated in the resistor during the discharge.

energy = ........................................... J [3]

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6 (a) A uniform magnetic field has constant flux density B. A straight wire of fixed length carries a current I at an angle θ to the magnetic field, as shown in Fig. 6.1.

magnetic fieldflux density B


I

Fig. 6.1

(i) The current I in the wire is changed, keeping the angle θ constant. On Fig. 6.2, sketch a graph to show the variation with current I of the force F on the

wire.

0

F

I0

Fig. 6.2 [2]

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(ii) The angle θ between the wire and the magnetic field is now varied. The current I is kept constant.

On Fig. 6.3, sketch a graph to show the variation with angle θ of the force F on the wire.

F

00

30 60 90

/ °

Fig. 6.3 [3]

(b) A uniform magnetic field is directed at right-angles to the rectangular surface PQRS of a slice of a conducting material, as shown in Fig. 6.4.

Q R

direction ofmovementof electrons

uniform magnetic field

SP

Fig. 6.4

Electrons, moving towards the side SR, enter the slice of conducting material. The electrons enter the slice at right-angles to side SR.

(i) Explain why, initially, the electrons do not travel in straight lines across the slice from side SR to side PQ.

..................................................................................................................................

..................................................................................................................................

............................................................................................................................ [2]

(ii) Explain to which side, PS or QR, the electrons tend to move.

..................................................................................................................................

..................................................................................................................................

............................................................................................................................ [2]

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7 (a) Explain what is meant by the root-mean-square (r.m.s.) value of an alternating voltage.

..........................................................................................................................................

..........................................................................................................................................

.................................................................................................................................... [2]

(b) An alternating voltage V is represented by the equation

V = 220 sin(120πt),

where V is measured in volts and t is in seconds.

For this alternating voltage, determine

(i) the peak voltage,

peak voltage = ........................................... V [1]

(ii) the r.m.s. voltage,

r.m.s. voltage = ........................................... V [1]

(iii) the frequency.

frequency = ......................................... Hz [1]

(c) The alternating voltage in (b) is applied across a resistor such that the mean power output from the resistor is 1.5 kW.

Calculate the resistance of the resistor.

resistance = .......................................... Ω [2]


ForExaminer’s

Use

8 Americium-241 is an artificially produced radioactive element that emits α-particles. A sample of americium-241 of mass 5.1 μg is found to have an activity of 5.9 × 105 Bq.

(a) Determine, for this sample of americium-241,

(i) the number of nuclei,

number = ............................................... [2]

(ii) the decay constant,

decay constant = ........................................ s–1 [2]

(iii) the half-life, in years.

half-life = .................................... years [2]

(b) Another radioactive element has a half-life of approximately 4 hours. Suggest why measurement of the mass and activity of a sample of this element is not

appropriate for the determination of its half-life.

..........................................................................................................................................

.................................................................................................................................... [1]

15

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Section B


9 (a) Negative feedback may be used in amplifier circuits. State

(i) what is meant by negative feedback,

..................................................................................................................................

..................................................................................................................................

............................................................................................................................ [2]

(ii) two effects of negative feedback on an amplifier incorporating an operational amplifier (op-amp).

1. ...............................................................................................................................

..................................................................................................................................

2. ...............................................................................................................................

.................................................................................................................................. [2]

(b) Fig. 9.1 is a circuit for an amplifier that is used with a microphone.

microphone

P

120 kΩ

R

V OUT

Fig. 9.1

The output potential difference VOUT is 4.4 V when the potential at point P is 62 mV.

Determine

(i) the gain of the amplifier,

gain = ............................................... [1]

17


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(ii) the resistance of the resistor R.

resistance = .......................................... Ω [2]

(c) The maximum potential produced by the microphone at point P on Fig. 9.1 is 95 mV. The power supply for the operational amplifier may be either +/– 5 V or +/– 9 V.

State which power supply should be used. Justify your answer quantitatively.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

.................................................................................................................................... [3]

18

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10 (a) State the name of an electrical sensing device that will respond to changes in

(i) length,

............................................................................................................................ [1]

(ii) pressure.

............................................................................................................................ [1]

(b) A relay is sometimes used as the output of a sensing circuit.

The output of a particular sensing circuit is either + 2 V or – 2 V.

On Fig. 10.1, draw symbols for a relay and any other necessary component so that the external circuit is switched on only when the output from the sensing circuit is + 2 V.

terminalsof externalcircuit

output fromsensing circuit

+2 V or –2 V

Fig. 10.1 [4]

19

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Use

[Turn over

11 Explain the main principles behind the generation of ultrasound to obtain diagnostic information about internal body structures.

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

.................................................................................................................................................

........................................................................................................................................... [6]

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12 A telephone link between two towns is to be provided using an optic fibre. The length of the optic fibre between the two towns is 75 km.

(a) State two changes that occur in a signal as it is transmitted along an optic fibre.

1. ......................................................................................................................................

..........................................................................................................................................

2. ......................................................................................................................................

.......................................................................................................................................... [2]

(b) The optic fibre has an attenuation per unit length of 1.6 dB km–1. The minimum permissible signal-to-noise power ratio in the fibre is 25 dB. The average noise power in the optic fibre is 6.1 × 10–19 W.

(i) Suggest one reason why power ratios are expressed in dB.

..................................................................................................................................

............................................................................................................................ [1]

(ii) The signal input power to the optic fibre is designed to be 6.5 mW. Determine whether repeater amplifiers are necessary in the optic fibre between the

two towns.

[5]




DC (LEO/SW) 23673/4© UCLES 2010 [Turn over






*1746825571*

PHYSICS 9702/41

Paper 4 A2 Structured Questions October/November 2010

1 hour 45 minutes




1

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3

9702/41/O/N/10© UCLES 2010 [Turn over

Formulae

uniformly accelerated motion, s = ut + 12 at 2

v2 = u2 + 2as





NmV

<c2>



v = ± ω √⎯ ⎯ ⎯ ⎯ ⎯ ⎯ (x02 – x 2)










t 12

4

9702/41/O/N/10© UCLES 2010

ForExaminer’s

Use

Section A


1 (a) Define gravitational field strength.

..........................................................................................................................................

...................................................................................................................................... [1]

(b) An isolated star has radius R. The mass of the star may be considered to be a point mass at the centre of the star.

The gravitational field strength at the surface of the star is gs.

On Fig. 1.1, sketch a graph to show the variation of the gravitational field strength of the star with distance from its centre. You should consider distances in the range R to 4R.

0R 2R 3R 4R

distance

0.2gs

0.4gs

0.6gs

0.8gs

gravitationalfield strength

surfaceof star

1.0gs

Fig. 1.1 [2]

(c) The Earth and the Moon may be considered to be spheres that are isolated in space with their masses concentrated at their centres.

The masses of the Earth and the Moon are 6.00 × 1024 kg and 7.40 × 1022 kg respectively.

The radius of the Earth is RE and the separation of the centres of the Earth and the Moon is 60 RE, as illustrated in Fig. 1.2.

Earthmass

6.00 x 1024 kg

Moonmass

7.40 x 1022 kg

RE

60 RE


5


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(i) Explain why there is a point between the Earth and the Moon at which the gravitational field strength is zero.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(ii) Determine the distance, in terms of RE, from the centre of the Earth at which the gravitational field strength is zero.

distance = ...........................................RE [3]

(iii) On the axes of Fig. 1.3, sketch a graph to show the variation of the gravitational field strength with position between the surface of the Earth and the surface of the Moon.

0


surfaceof Earth

surfaceof Moon

distance

Fig. 1.3 [3]

6

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2 (a) (i) State the basic assumption of the kinetic theory of gases that leads to the conclusion that the potential energy between the atoms of an ideal gas is zero.

..................................................................................................................................

.............................................................................................................................. [1]

(ii) State what is meant by the internal energy of a substance.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(iii) Explain why an increase in internal energy of an ideal gas is directly related to a rise in temperature of the gas.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(b) A fixed mass of an ideal gas undergoes a cycle PQRP of changes as shown in Fig. 2.1.

050 10 15 20 25 30

2

4

6

volume/ 10–4 m3

pressure / 105 Pa

8

10

Q

P

R

Fig. 2.1

7


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(i) State the change in internal energy of the gas during one complete cycle PQRP.

change = ............................................. J [1]

(ii) Calculate the work done on the gas during the change from P to Q.

work done = .............................................. J [2]

(iii) Some energy changes during the cycle PQRP are shown in Fig. 2.2.

changework done on gas

/ Jheating supplied

to gas / Jincrease in

internal energy / J

P Q

Q R

R P

.............................

0

.............................

–600

+720

+480

.............................

.............................

.............................

Fig. 2.2

Complete Fig. 2.2 to show all of the energy changes. [3]

8

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3 A student sets up the apparatus illustrated in Fig. 3.1 in order to investigate the oscillations of a metal cube suspended on a spring.

variable-frequencyoscillator

thread

pulley

spring

metalcube

Fig. 3.1

The amplitude of the vibrations produced by the oscillator is constant. The variation with frequency of the amplitude of the oscillations of the metal cube is shown

in Fig. 3.2.

042 6 8 10

5

10

15

amplitude/ mm

frequency / Hz

20

Fig. 3.2

(a) (i) State the phenomenon illustrated in Fig. 3.2.

.............................................................................................................................. [1]

(ii) For the maximum amplitude of vibration, state the magnitudes of the amplitude and the frequency.

amplitude = ............................................. mm

frequency = ............................................... Hz [1]

9


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(b) The oscillations of the metal cube of mass 150 g may be assumed to be simple harmonic.

Use your answers in (a)(ii) to determine, for the metal cube,

(i) its maximum acceleration,

acceleration = ...................................... m s–2 [3]

(ii) the maximum resultant force on the cube.

force = .......................................... N [2]

(c) Some very light feathers are attached to the top surface of the cube so that the feathers extend outwards, beyond the vertical sides of the cube.

The investigation is now repeated. On Fig. 3.2, draw a line to show the new variation with frequency of the amplitude of

vibration for frequencies between 2 Hz and 10 Hz. [2]

10

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4 (a) Define capacitance.

..........................................................................................................................................

...................................................................................................................................... [1]

(b) An isolated metal sphere has a radius r. When charged to a potential V, the charge on the sphere is q.

The charge may be considered to act as a point charge at the centre of the sphere.

(i) State an expression, in terms of r and q, for the potential V of the sphere.

.............................................................................................................................. [1]

(ii) This isolated sphere has capacitance. Use your answers in (a) and (b)(i) to show that the capacitance of the sphere is proportional to its radius.

[1]

(c) The sphere in (b) has a capacitance of 6.8 pF and is charged to a potential of 220 V.

Calculate

(i) the radius of the sphere,

radius = ........................................... m [3]

11


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(ii) the charge, in coulomb, on the sphere.

charge = ........................................... C [1]

(d) A second uncharged metal sphere is brought up to the sphere in (c) so that they touch. The combined capacitance of the two spheres is 18 pF.

Calculate

(i) the potential of the two spheres,

potential = ............................................ V [1]

(ii) the change in the total energy stored on the spheres when they touch.

change = ........................................... J [3]

12

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5 Positive ions are travelling through a vacuum in a narrow beam. The ions enter a region of uniform magnetic field of flux density B and are deflected in a semi-circular arc, as shown in Fig. 5.1.

12.8 cm

detector

beam ofpositive ions

uniform magneticfield

Fig. 5.1

The ions, travelling with speed 1.40 × 105 m s–1, are detected at a fixed detector when the diameter of the arc in the magnetic field is 12.8 cm.

(a) By reference to Fig. 5.1, state the direction of the magnetic field.

...................................................................................................................................... [1]

(b) The ions have mass 20 u and charge +1.6 × 10–19 C. Show that the magnetic flux density is 0.454 T. Explain your working.

[3]

13


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(c) Ions of mass 22 u with the same charge and speed as those in (b) are also present in the beam.

(i) On Fig. 5.1, sketch the path of these ions in the magnetic field of magnetic flux density 0.454 T. [1]

(ii) In order to detect these ions at the fixed detector, the magnetic flux density is changed.

Calculate this new magnetic flux density.

magnetic flux density = ............................................. T [2]

14

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6 A simple iron-cored transformer is illustrated in Fig. 6.1.

outputinput

primarycoil

secondarycoil

ironcore

Fig. 6.1

(a) (i) State why the primary and secondary coils are wound on a core made of iron.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [1]

(ii) Suggest why thermal energy is generated in the core when the transformer isin use.

..................................................................................................................................

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [3]

15


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(b) The root-mean-square (r.m.s.) voltage and current in the primary coil are VP and IP respectively.

The r.m.s. voltage and current in the secondary coil are VS and IS respectively.

(i) Explain, by reference to direct current, what is meant by the root-mean-square value of an alternating current.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(ii) Show that, for an ideal transformer,

VS

VP

= IP

IS

.

[2]

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7 (a) State an effect, one in each case, that provides evidence for

(i) the wave nature of a particle,

.............................................................................................................................. [1]

(ii) the particulate nature of electromagnetic radiation.

.............................................................................................................................. [1]

(b) Four electron energy levels in an atom are shown in Fig. 7.1.

electronenergy

–0.87 × 10–19 J

–1.36 × 10–19 J

–2.42 × 10–19 J

–5.44 × 10–19 J


An emission spectrum is associated with the electron transitions between these energy levels.

For this spectrum,

(i) state the number of lines,

.............................................................................................................................. [1]

(ii) calculate the minimum wavelength.

wavelength = ........................................... m [2]

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8 In some power stations, nuclear fission is used as a source of energy.

(a) State what is meant by nuclear fission.

.........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [2]

(b) The nuclear fission reaction produces neutrons. In the power station, the neutrons may be absorbed by rods made of boron-10.

Complete the nuclear equation for the absorption of a single neutron by a boron-10 nucleus with the emission of an a-particle.

105B + ...................... .......

3Li + ...................... [3]

(c) Suggest why, when neutrons are absorbed in the boron rods, the rods become hot as a result of this nuclear reaction.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [3]

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Section B


9 An amplifier circuit incorporating an operational amplifier (op-amp) is shown in Fig. 9.1.

R2

VIN

VOUTR1

–

–9 V

+9 V

+

Fig. 9.1

(a) State

(i) the name of this type of amplifier circuit,

.............................................................................................................................. [1]

(ii) the gain G in terms of resistances R1 and R2.

.............................................................................................................................. [1]

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(b) The value of R1 is 820 Ω. The resistor of resistance R2 is replaced with a light-dependent resistor (LDR).

The input potential difference VIN is 15 mV. Calculate the output potential difference VOUT for the LDR having a resistance of

(i) 100 Ω (the LDR is in sunlight),

VOUT = ............................................. V [2]

(ii) 1.0 MΩ (the LDR is in darkness).

VOUT = ........................................... V [1]

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10 (a) (i) State what is meant by the acoustic impedance of a medium.

..................................................................................................................................

.............................................................................................................................. [1]

(ii) Data for some media are given in Fig. 10.1.

medium speed of ultrasound/ m s–1

acoustic impedance/ kg m–2 s–1

airgelsoft tissuebone

330150016004100

4.3 × 102

1.5 × 106

1.6 × 106

7.0 × 106

Fig. 10.1

Use data from Fig. 10.1 to calculate a value for the density of bone.

density = .................................... kg m–3 [1]

(b) A parallel beam of ultrasound has intensity I. It is incident at right-angles to a boundary between two media, as shown in Fig. 10.2.

transmittedintensity IT

reflectedintensity IR

incidentintensity I

acoustic impedance Z2acoustic impedance Z1

boundary

Fig. 10.2

The media have acoustic impedances of Z1 and Z2. The transmitted intensity of the ultrasound beam is IT and the reflected intensity is IR.

(i) State the relation between I, IT and IR.

.............................................................................................................................. [1]

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(ii) The reflection coefficient a is given by the expression

a = (Z2 – Z1)2

(Z2 + Z1)2.

Use data from Fig. 10.1 to determine the reflection coefficient a for a boundary between

1. gel and soft tissue,

a = .................................................. [2]

2. air and soft tissue.

a = .................................................. [1]

(c) By reference to your answers in (b)(ii), explain the use of a gel on the surface of skin during ultrasound diagnosis.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [3]

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11 (a) Wire pairs provide one means of communication but they are subject to high levels of noise and attenuation.

Explain what is meant by

(i) noise,

..................................................................................................................................

.............................................................................................................................. [1]

(ii) attenuation.

..................................................................................................................................

.............................................................................................................................. [1]

(b) A microphone is connected to a receiver using a wire pair, as shown in Fig. 11.1.

receiver

wire pair

microphone

Fig. 11.1

The wire pair has an attenuation per unit length of 12 dB km–1. The noise power in the wire pair is 3.4 × 10–9 W.

The microphone produces a signal power of 2.9 lW.

(i) Calculate the maximum length of the wire pair so that the minimum signal-to-noise ratio is 24 dB.

length = ............................................ m [4]

(ii) Communication over distances greater than that calculated in (i) is required. Suggest how the circuit of Fig. 11.1 may be modified so that the minimum

signal-to-noise ratio at the receiver is not reduced.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

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12 (a) Outline the principles of the use of a geostationary satellite for communication on Earth.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [4]

Question 12 continues on the next page.

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(b) Polar-orbiting satellites are also used for communication on Earth. State and explain one advantage and one disadvantage of polar-orbiting satellites as

compared with geostationary satellites.

advantage: ......................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

disadvantage: ..................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... [4]


DC (AC/SW) 34437© UCLES 2010 [Turn over






*2900417311*

PHYSICS 9702/42


1 hour 45 minutes




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3


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v2 = u2 + 2as





NmV

<c2>



v = ± ω √⎯ ⎯ ⎯ ⎯ ⎯ ⎯ (x02 – x 2)










t 12

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Section A


1 (a) Define gravitational field strength.

..........................................................................................................................................

...................................................................................................................................... [1]

(b) An isolated star has radius R. The mass of the star may be considered to be a point mass at the centre of the star.

The gravitational field strength at the surface of the star is gs.

On Fig. 1.1, sketch a graph to show the variation of the gravitational field strength of the star with distance from its centre. You should consider distances in the range R to 4R.

0R 2R 3R 4R

distance

0.2gs

0.4gs

0.6gs

0.8gs


surfaceof star

1.0gs

Fig. 1.1 [2]

(c) The Earth and the Moon may be considered to be spheres that are isolated in space with their masses concentrated at their centres.

The masses of the Earth and the Moon are 6.00 × 1024 kg and 7.40 × 1022 kg respectively.

The radius of the Earth is RE and the separation of the centres of the Earth and the Moon is 60 RE, as illustrated in Fig. 1.2.

Earthmass

6.00 x 1024 kg

Moonmass

7.40 x 1022 kg

RE

60 RE


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(i) Explain why there is a point between the Earth and the Moon at which the gravitational field strength is zero.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(ii) Determine the distance, in terms of RE, from the centre of the Earth at which the gravitational field strength is zero.

distance = ...........................................RE [3]

(iii) On the axes of Fig. 1.3, sketch a graph to show the variation of the gravitational field strength with position between the surface of the Earth and the surface of the Moon.

0


surfaceof Earth

surfaceof Moon

distance

Fig. 1.3 [3]

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2 (a) (i) State the basic assumption of the kinetic theory of gases that leads to the conclusion that the potential energy between the atoms of an ideal gas is zero.

..................................................................................................................................

.............................................................................................................................. [1]

(ii) State what is meant by the internal energy of a substance.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(iii) Explain why an increase in internal energy of an ideal gas is directly related to a rise in temperature of the gas.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(b) A fixed mass of an ideal gas undergoes a cycle PQRP of changes as shown in Fig. 2.1.

050 10 15 20 25 30

2

4

6

volume/ 10–4 m3

pressure / 105 Pa

8

10

Q

P

R

Fig. 2.1

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(i) State the change in internal energy of the gas during one complete cycle PQRP.

change = ............................................. J [1]

(ii) Calculate the work done on the gas during the change from P to Q.

work done = .............................................. J [2]

(iii) Some energy changes during the cycle PQRP are shown in Fig. 2.2.

changework done on gas

/ Jheating supplied

to gas / Jincrease in

internal energy / J

P Q

Q R

R P

.............................

0

.............................

–600

+720

+480

.............................

.............................

.............................

Fig. 2.2

Complete Fig. 2.2 to show all of the energy changes. [3]

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3 A student sets up the apparatus illustrated in Fig. 3.1 in order to investigate the oscillations of a metal cube suspended on a spring.

variable-frequencyoscillator

thread

pulley

spring

metalcube

Fig. 3.1

The amplitude of the vibrations produced by the oscillator is constant. The variation with frequency of the amplitude of the oscillations of the metal cube is shown

in Fig. 3.2.

042 6 8 10

5

10

15

amplitude/ mm

frequency / Hz

20

Fig. 3.2

(a) (i) State the phenomenon illustrated in Fig. 3.2.

.............................................................................................................................. [1]

(ii) For the maximum amplitude of vibration, state the magnitudes of the amplitude and the frequency.

amplitude = ............................................. mm

frequency = ............................................... Hz [1]

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(b) The oscillations of the metal cube of mass 150 g may be assumed to be simple harmonic.

Use your answers in (a)(ii) to determine, for the metal cube,

(i) its maximum acceleration,

acceleration = ...................................... m s–2 [3]

(ii) the maximum resultant force on the cube.

force = .......................................... N [2]

(c) Some very light feathers are attached to the top surface of the cube so that the feathers extend outwards, beyond the vertical sides of the cube.

The investigation is now repeated. On Fig. 3.2, draw a line to show the new variation with frequency of the amplitude of

vibration for frequencies between 2 Hz and 10 Hz. [2]

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4 (a) Define capacitance.

..........................................................................................................................................

...................................................................................................................................... [1]

(b) An isolated metal sphere has a radius r. When charged to a potential V, the charge on the sphere is q.

The charge may be considered to act as a point charge at the centre of the sphere.

(i) State an expression, in terms of r and q, for the potential V of the sphere.

.............................................................................................................................. [1]

(ii) This isolated sphere has capacitance. Use your answers in (a) and (b)(i) to show that the capacitance of the sphere is proportional to its radius.

[1]

(c) The sphere in (b) has a capacitance of 6.8 pF and is charged to a potential of 220 V.

Calculate

(i) the radius of the sphere,

radius = ........................................... m [3]

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(ii) the charge, in coulomb, on the sphere.

charge = ........................................... C [1]

(d) A second uncharged metal sphere is brought up to the sphere in (c) so that they touch. The combined capacitance of the two spheres is 18 pF.

Calculate

(i) the potential of the two spheres,

potential = ............................................ V [1]

(ii) the change in the total energy stored on the spheres when they touch.

change = ........................................... J [3]

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5 Positive ions are travelling through a vacuum in a narrow beam. The ions enter a region of uniform magnetic field of flux density B and are deflected in a semi-circular arc, as shown in Fig. 5.1.

12.8 cm

detector

beam ofpositive ions

uniform magneticfield

Fig. 5.1

The ions, travelling with speed 1.40 × 105 m s–1, are detected at a fixed detector when the diameter of the arc in the magnetic field is 12.8 cm.

(a) By reference to Fig. 5.1, state the direction of the magnetic field.

...................................................................................................................................... [1]

(b) The ions have mass 20 u and charge +1.6 × 10–19 C. Show that the magnetic flux density is 0.454 T. Explain your working.

[3]

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(c) Ions of mass 22 u with the same charge and speed as those in (b) are also present in the beam.

(i) On Fig. 5.1, sketch the path of these ions in the magnetic field of magnetic flux density 0.454 T. [1]

(ii) In order to detect these ions at the fixed detector, the magnetic flux density is changed.

Calculate this new magnetic flux density.

magnetic flux density = ............................................. T [2]

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6 A simple iron-cored transformer is illustrated in Fig. 6.1.

outputinput

primarycoil

secondarycoil

ironcore

Fig. 6.1

(a) (i) State why the primary and secondary coils are wound on a core made of iron.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [1]

(ii) Suggest why thermal energy is generated in the core when the transformer isin use.

..................................................................................................................................

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [3]

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(b) The root-mean-square (r.m.s.) voltage and current in the primary coil are VP and IP respectively.

The r.m.s. voltage and current in the secondary coil are VS and IS respectively.

(i) Explain, by reference to direct current, what is meant by the root-mean-square value of an alternating current.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(ii) Show that, for an ideal transformer,

VS

VP

= IP

IS

.

[2]

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7 (a) State an effect, one in each case, that provides evidence for

(i) the wave nature of a particle,

.............................................................................................................................. [1]

(ii) the particulate nature of electromagnetic radiation.

.............................................................................................................................. [1]

(b) Four electron energy levels in an atom are shown in Fig. 7.1.

electronenergy

–0.87 × 10–19 J

–1.36 × 10–19 J

–2.42 × 10–19 J

–5.44 × 10–19 J


An emission spectrum is associated with the electron transitions between these energy levels.

For this spectrum,

(i) state the number of lines,

.............................................................................................................................. [1]

(ii) calculate the minimum wavelength.

wavelength = ........................................... m [2]

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8 In some power stations, nuclear fission is used as a source of energy.

(a) State what is meant by nuclear fission.

.........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [2]

(b) The nuclear fission reaction produces neutrons. In the power station, the neutrons may be absorbed by rods made of boron-10.

Complete the nuclear equation for the absorption of a single neutron by a boron-10 nucleus with the emission of an a-particle.

105B + ...................... .......

3Li + ...................... [3]

(c) Suggest why, when neutrons are absorbed in the boron rods, the rods become hot as a result of this nuclear reaction.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [3]

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Section B


9 An amplifier circuit incorporating an operational amplifier (op-amp) is shown in Fig. 9.1.

R2

VIN

VOUTR1

–

–9 V

+9 V

+

Fig. 9.1

(a) State

(i) the name of this type of amplifier circuit,

.............................................................................................................................. [1]

(ii) the gain G in terms of resistances R1 and R2.

.............................................................................................................................. [1]

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(b) The value of R1 is 820 Ω. The resistor of resistance R2 is replaced with a light-dependent resistor (LDR).

The input potential difference VIN is 15 mV. Calculate the output potential difference VOUT for the LDR having a resistance of

(i) 100 Ω (the LDR is in sunlight),

VOUT = ............................................. V [2]

(ii) 1.0 MΩ (the LDR is in darkness).

VOUT = ........................................... V [1]

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10 (a) (i) State what is meant by the acoustic impedance of a medium.

..................................................................................................................................

.............................................................................................................................. [1]

(ii) Data for some media are given in Fig. 10.1.

medium speed of ultrasound/ m s–1

acoustic impedance/ kg m–2 s–1

airgelsoft tissuebone

330150016004100

4.3 × 102

1.5 × 106

1.6 × 106

7.0 × 106

Fig. 10.1

Use data from Fig. 10.1 to calculate a value for the density of bone.

density = .................................... kg m–3 [1]

(b) A parallel beam of ultrasound has intensity I. It is incident at right-angles to a boundary between two media, as shown in Fig. 10.2.

transmittedintensity IT

reflectedintensity IR

incidentintensity I

acoustic impedance Z2acoustic impedance Z1

boundary

Fig. 10.2

The media have acoustic impedances of Z1 and Z2. The transmitted intensity of the ultrasound beam is IT and the reflected intensity is IR.

(i) State the relation between I, IT and IR.

.............................................................................................................................. [1]

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(ii) The reflection coefficient a is given by the expression

a = (Z2 – Z1)2

(Z2 + Z1)2.

Use data from Fig. 10.1 to determine the reflection coefficient a for a boundary between

1. gel and soft tissue,

a = .................................................. [2]

2. air and soft tissue.

a = .................................................. [1]

(c) By reference to your answers in (b)(ii), explain the use of a gel on the surface of skin during ultrasound diagnosis.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [3]

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11 (a) Wire pairs provide one means of communication but they are subject to high levels of noise and attenuation.

Explain what is meant by

(i) noise,

..................................................................................................................................

.............................................................................................................................. [1]

(ii) attenuation.

..................................................................................................................................

.............................................................................................................................. [1]

(b) A microphone is connected to a receiver using a wire pair, as shown in Fig. 11.1.

receiver

wire pair

microphone

Fig. 11.1

The wire pair has an attenuation per unit length of 12 dB km–1. The noise power in the wire pair is 3.4 × 10–9 W.

The microphone produces a signal power of 2.9 lW.

(i) Calculate the maximum length of the wire pair so that the minimum signal-to-noise ratio is 24 dB.

length = ............................................ m [4]

(ii) Communication over distances greater than that calculated in (i) is required. Suggest how the circuit of Fig. 11.1 may be modified so that the minimum

signal-to-noise ratio at the receiver is not reduced.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

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12 (a) Outline the principles of the use of a geostationary satellite for communication on Earth.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [4]

Question 12 continues on the next page.

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(b) Polar-orbiting satellites are also used for communication on Earth. State and explain one advantage and one disadvantage of polar-orbiting satellites as

compared with geostationary satellites.

advantage: ......................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

disadvantage: ..................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... [4]

This document consists of 23 printed pages and 1 blank page.

DC (AC/SW) 23675/6© UCLES 2010 [Turn over






*8365187983*

PHYSICS 9702/43


1 hour 45 minutes




1

2

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4

5

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7

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12

Total


3


Formulae


v2 = u2 + 2as





NmV

<c2>



v = ± ω √⎯ ⎯ ⎯ ⎯ ⎯ ⎯ (x02 – x 2)










t 12

4

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ForExaminer’s

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Section A


1 A planet of mass m is in a circular orbit of radius r about the Sun of mass M, as illustrated in Fig. 1.1.

Sunmass M

planet

r

mass m

Fig. 1.1

The magnitude of the angular velocity and the period of revolution of the planet about the Sun are x and T respectively.

(a) State

(i) what is meant by angular velocity,

..................................................................................................................................

.................................................................................................................................. .............................................................................................................................. [2]

(ii) the relation between x and T.

.............................................................................................................................. [1]

(b) Show that, for a planet in a circular orbit of radius r, the period T of the orbit is given by the expression

T 2 = cr 3

where c is a constant. Explain your working.

[4]

5


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(c) Data for the planets Venus and Neptune are given in Fig. 1.2.

planet r / 108 km T / years

VenusNeptune

1.0845.0

0.615

Fig. 1.2

Assume that the orbits of both planets are circular.

(i) Use the expression in (b) to calculate the value of T for Neptune.

T = ....................................... years [2]

(ii) Determine the linear speed of Venus in its orbit.

speed = ..................................... km s–1 [2]

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2 (a) State the basic assumptions of the kinetic theory of gases.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... ...................................................................................................................................... [4]

(b) Use equations for the pressure of an ideal gas to deduce that the average translational kinetic energy <EK> of a molecule of an ideal gas is given by the expression

<EK> = T

where R is the molar gas constant, NA is the Avogadro constant and T is the thermodynamic temperature of the gas.

[3]

(c) A deuterium nucleus 21H and a proton collide. A nuclear reaction occurs, represented by the equation

21H + 11p 32He + c.

(i) State and explain whether the reaction represents nuclear fission or nuclear fusion.

..................................................................................................................................

..................................................................................................................................

............................................................................................................................. [2]

32

R NA

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(ii) For the reaction to occur, the minimum total kinetic energy of the deuterium nucleus and the proton is 2.4 × 10–14 J.

Assuming that a sample of a mixture of deuterium nuclei and protons behaves as an ideal gas, calculate the temperature of the sample for this reaction to occur.

temperature = ............................................. K [3]

(iii) Suggest why the assumption made in (ii) may not be valid.

..................................................................................................................................

.............................................................................................................................. [1]

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3 A cylinder and piston, used in a car engine, are illustrated in Fig. 3.1.

C

A

D

cylinder

piston

B

Fig. 3.1

The vertical motion of the piston in the cylinder is assumed to be simple harmonic. The top surface of the piston is at AB when it is at its lowest position; it is at CD when at its

highest position, as marked in Fig. 3.1.

(a) The displacement d of the piston may be represented by the equation

d = – 4.0 cos(220t )

where d is measured in centimetres.

(i) State the distance between the lowest position AB and the highest position CD of the top surface of the piston.

distance = .......................................... cm [1]

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(ii) Determine the number of oscillations made per second by the piston.

number = ................................................ [2]

(iii) On Fig. 3.1, draw a line to represent the top surface of the piston in the position where the speed of the piston is maximum. [1]

(iv) Calculate the maximum speed of the piston.

speed = ..................................... cm s–1 [2]

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(b) The engine of a car has several cylinders. Three of these cylinders are shown in Fig. 3.2.

C

A

D

B

X Y Z

Fig. 3.2

X is the same cylinder and piston as in Fig. 3.1. Y and Z are two further cylinders, with the lowest and the highest positions of the top

surface of each piston indicated. The pistons in the cylinders each have the same frequency of oscillation, but they are

not in phase. At a particular instant in time, the position of the top of the piston in cylinder X is as

shown.

(i) In cylinder Y, the oscillations of the piston lead those of the piston in cylinder X by a phase angle of 120° (2

3p rad).

Complete the diagram of cylinder Y, for this instant, by drawing

1. a line to show the top surface of the piston, [1]

2. an arrow to show the direction of movement of the piston. [1]

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(ii) In cylinder Z, the oscillations of the piston lead those of the piston in cylinder X by a phase angle of 240° (4

3p rad).

Complete the diagram of cylinder Z, for this instant, by drawing

1. a line to show the top surface of the piston, [1]

2. an arrow to show the direction of movement of the piston. [1]

(iii) For the piston in cylinder Y, calculate its speed for this instant.

speed = ..................................... cm s–1 [2]

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4 (a) (i) State what is meant by electric potential at a point.

..................................................................................................................................

..................................................................................................................................

............................................................................................................................. [2]

(ii) Define capacitance.

..................................................................................................................................

............................................................................................................................. [1]

(b) The variation of the potential V of an isolated metal sphere with charge Q on its surface is shown in Fig. 4.1.

00 0.5 1.0 1.5 2.0 2.5 3.0

50

100

150

V / kV

Q / µC

200

Fig. 4.1

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An isolated metal sphere has capacitance.

Use Fig. 4.1 to determine

(i) the capacitance of the sphere,

capacitance = ............................................. F [2]

(ii) the electric potential energy stored on the sphere when charged to a potential of 150 kV.

energy = ............................................. J [2]

(c) A spark reduces the potential of the sphere from 150 kV to 75 kV. Calculate the energy lost from the sphere.

energy = ............................................. J [2]

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5 The poles of a horseshoe magnet measure 5.0 cm × 2.4 cm, as shown in Fig. 5.1.

A

pole pieceof magnet

direction ofmovement

of wire

copper wire

5.0 cm

2.4 cm

Fig. 5.1 The uniform magnetic flux density between the poles of the magnet is 89 mT. Outside the

region of the poles, the magnetic flux density is zero. A stiff copper wire is connected to a sensitive ammeter of resistance 0.12 Ω. A student moves

the wire at a constant speed of 1.8 m s–1 between the poles in a direction parallel to the faces of the poles.

(a) Calculate the magnetic flux between the poles of the magnet.

magnetic flux = .......................................... Wb [2]

(b) (i) Use your answer in (a) to determine, for the wire moving between the poles of the magnet, the e.m.f. induced in the wire.

e.m.f. = ............................................. V [3]

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(ii) Show that the reading on the ammeter is approximately 70 mA.

[1]

(c) By reference to Lenz’s law, a force acts on the wire to oppose the motion of the wire. The student who moved the wire between the poles of the magnet claims not to have

felt this force. Explain quantitatively a reason for this claim.

..........................................................................................................................................

..................................................................................................................................... [3]

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6 The variation with time t of the current I in a resistor is shown in Fig. 6.1.

0

I

t

Fig. 6.1

The variation of the current with time is sinusoidal.

(a) Explain why, although the current is not in one direction only, power is converted in the resistor.

..........................................................................................................................................

..........................................................................................................................................

..................................................................................................................................... [2]

(b) Using the relation between root-mean-square (r.m.s.) current and peak current, deduce the value of the ratio

average power converted in the resistore .

maximum power converted in the resistor

ratio = ................................................ [3]

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7 Electrons are moving through a vacuum in a narrow beam. The electrons have speed v. The electrons enter a region of uniform magnetic field of flux density B. Initially, the electrons

are travelling at a right-angle to the magnetic field. The path of a single electron is shown in Fig. 7.1.

electron

speed v

region of magnetic fieldflux density B

Fig. 7.1

The electrons follow a curved path in the magnetic field.

A uniform electric field of field strength E is now applied in the same region as the magnetic field.

The electrons pass undeviated through the region of the two fields. Gravitational effects may be neglected.

(a) Derive a relation between v, E and B for the electrons not to be deflected. Explain your working.

..........................................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... ..........................................................................................................................................

..................................................................................................................................... [3]

(b) An α-particle has speed v and approaches the region of the two fields along the same path as the electron. Describe and explain the path of the α-particle as it passes through the region of the two fields.

.......................................................................................................................................... ..........................................................................................................................................

..................................................................................................................................... [2]

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Use

8 (a) By reference to the photoelectric effect, state what is meant by the threshold frequency.

..........................................................................................................................................

..........................................................................................................................................

..................................................................................................................................... [2]

(b) The surface of a zinc plate has a work function of 5.8 × 10–19 J. In a particular laboratory experiment, ultraviolet light of wavelength 120 nm is incident

on the zinc plate. A photoelectric current I is detected. In order to view the apparatus more clearly, a second lamp emitting light of wavelength

450 nm is switched on. No change is made to the ultraviolet lamp. Using appropriate calculations, state and explain the effect on the photoelectric current

of switching on this second lamp.

..........................................................................................................................................

..................................................................................................................................... [4]

19


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Use

Section B


9 (a) (i) State, with reference to X-ray images, what is meant by sharpness.

..................................................................................................................................

.............................................................................................................................. [1]

(ii) Describe briefly two factors that affect the sharpness of an X-ray image.

1. ...............................................................................................................................

..................................................................................................................................

2. ...............................................................................................................................

.................................................................................................................................. [3]

(b) An X-ray image is taken of the skull of a patient. Another patient has a CT scan of his head.

By reference to the formation of the image in each case, suggest why the exposure to radiation differs between the two imaging techniques.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [4]

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10 (a) State three properties of an ideal operational amplifier (op-amp).

1. ......................................................................................................................................

2. ......................................................................................................................................

3. ...................................................................................................................................... [3]

(b) A circuit incorporating an ideal op-amp is to be used to indicate whether a door is open or closed.

Resistors, each of resistance R, are connected to the inputs of the op-amp, as shown in Fig. 10.1.

R

R

RRS

–

–9 V

+9 V

+3 V

+

R

Fig. 10.1

The switch S is attached to the door so that, when the door is open, the switch is open. The switch closes when the door is closed.

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ForExaminer’s

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(i) Explain why the polarity of the output of the op-amp changes when the switch closes.

..................................................................................................................................

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [3]

(ii) A red light-emitting diode (LED) is to be used to indicate when the door is open. A green LED is to indicate when the door is closed.

On Fig. 10.1,

1. draw symbols for the LEDs to show how they are connected to the output of the op-amp, [1]

2. identify the green LED with the letter G. [1]

Please turn over for Question 11.

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ForExaminer’s

Use

11 The linear attenuation (absorption) coefficient µ for X-ray radiation in bone, fat and muscle is given in Fig. 11.1.

µ / cm–1

bonefatmuscle

2.90.900.95

Fig. 11.1

(a) A parallel X-ray beam of intensity I0 is incident either on some bone or on some muscle.

The emergent beam has intensity I.

Calculate the ratio II0

for a thickness of (i) 1.5 cm of bone,

ratio = ................................................ [2]

(ii) 4.6 cm of muscle.

ratio = ................................................ [1]

(b) Suggest why, on an X-ray plate, the contrast between bone and muscle is much greater than that between fat and muscle.

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [3]

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Use

12 (a) Data may be transmitted as an analogue signal or as a digital signal.

(i) Explain what is meant by

1. an analogue signal,

..................................................................................................................................

..................................................................................................................................

..................................................................................................................................

2. a digital signal.

..................................................................................................................................

..................................................................................................................................

.................................................................................................................................. [3] (ii) State two advantages of the transmission of data in digital form.

1. ...............................................................................................................................

..................................................................................................................................

2. ...............................................................................................................................

.................................................................................................................................. [2]

(b) The block diagram of Fig. 12.1 represents a system for the digital transmission of analogue data.

analoguesignal

ADCmulti-channel cable

DAC output

Fig. 12.1

(i) Describe the function of the ADC (analogue-to-digital converter).

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(ii) Suggest why the transmission cable has a number of channels.

..................................................................................................................................

............................................................................................................................. [1]

simple harmonic motion, a = – ω2x velocity of particle in s.h.m., v = v ... kinetic energy e k 2...

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