Cambridge International Examinations

Cambridge International Advanced Subsidiary and Advanced Level

* 7 3 1 4 7 0 8 5 3 9 *

PHYSICS 9702/42
Paper 4 A Level Structured Questions October/November 2016
2 hours
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.

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Write in dark blue or black pen.
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Answer all questions.

Electronic calculators may be used.

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.

This document consists of 24 printed pages.

DC (RW/JG) 116303/4
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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

1
( = 8.99 × 109 m F−1)
4πε0
elementary charge e = 1.60 × 10−19 C

the Planck constant h = 6.63 × 10−34 J s

unified atomic mass unit 1 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

1
uniformly accelerated motion s = ut + 2 at 2
v 2 = u 2 + 2as

work done on/by a gas W = p ΔV

Gm
gravitational potential φ =−
r

hydrostatic pressure p = ρgh

1 Nm 2
pressure of an ideal gas p= 3 〈c 〉
V
simple harmonic motion a = − ω 2x

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

v =±ω√ 
(x02 – x 2)
fsv
Doppler effect fo =
v ± vs

Q
electric potential V=
4πε0r

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

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

1
energy of charged capacitor W = 2 QV

electric current I = Anvq

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

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

BI
Hall voltage VH =
ntq

alternating current/voltage x = x0 sin ω t

radioactive decay x = x0 exp(−λt )

0.693
decay constant λ=
t 1
2

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Answer all the questions in the spaces provided.

1 (a) Define gravitational field strength.

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

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

(b) The nearest star to the Sun is Proxima Centauri.

This star has a mass of 2.5 × 1029 kg and is a distance of 4.0 × 1013 km from the Sun.
The Sun has a mass of 2.0 × 1030 kg.

(i) State why Proxima Centauri may be assumed to be a point mass when viewed from the
Sun.

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

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

(ii) Calculate

1. the gravitational field strength due to Proxima Centauri at a distance of 4.0 × 1013 km,

field strength = ............................................... N kg–1 [2]

2. the gravitational force of attraction between the Sun and Proxima Centauri.

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

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(c) Suggest quantitatively why it may be assumed that the Sun is isolated in space from other
stars.

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

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

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

[Total: 8]

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2 (a) The equation of state for an ideal gas of volume V at pressure p is

pV = nRT

where R is the molar gas constant.

State what is meant by

(i) the symbol n,

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

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

(ii) the symbol T.

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

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

(b) An ideal gas is held in a container of volume 2.4 × 103 cm3 at pressure 4.9 × 105 Pa.
The temperature of the gas is 100 °C.

Show that the number of molecules of the gas in the container is 2.3 × 1023.

[3]

(c) Use data from (b) to estimate the mean distance between molecules in the gas.

mean distance = .................................................... cm [3]

[Total: 8]
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3 (a) State what is meant by the internal energy of a system.

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

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

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

(b) Explain, by reference to work done and heating, whether the internal energy of the following
increases, decreases or remains constant:

(i) the gas in a toy balloon when the balloon bursts suddenly,

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

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

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

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

(ii) ice melting at constant temperature and at atmospheric pressure to form water that is
more dense than the ice.

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

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

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

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

[Total: 8]

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4 A mass hangs vertically from a fixed point by means of a spring, as shown in Fig. 4.1.

spring
l

mass

Fig. 4.1

The mass is displaced vertically and then released. The subsequent oscillations of the mass are
simple harmonic.

The variation with time t of the length l of the spring is shown in Fig. 4.2.

18

17

16
l / cm
15

14

13

12
0 0.1 0.2 0.3 0.4 0.5 0.6
t /s

Fig. 4.2

(a) Use Fig. 4.2 to

(i) state two values of t at which the mass is moving downwards with maximum speed,

t = ................................. s and t = ................................. s [1]

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(ii) determine, for these oscillations, the angular frequency ω,

ω = .............................................. rad s–1 [2]

(iii) show that the maximum speed of the mass is 0.42 m s–1.

[2]

(b) Use data from Fig. 4.2 and (a)(iii) to sketch, on the axes of Fig. 4.3, the variation with
displacement x from the equilibrium position of the velocity v of the mass.

0.5

0.4
v / m s–1
0.3

0.2

0.1

0
–4 –3 –2 –1 0 1 2 3 4
–0.1 x / cm

–0.2

–0.3

–0.4

–0.5

Fig. 4.3 [3]

[Total: 8]
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5 Ultrasound may be used to obtain information about internal body structures.

(a) Suggest why the ultrasound from the transducer is pulsed.

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

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

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

(b) (i) State what is meant by specific acoustic impedance.

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

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

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

(ii) A parallel beam of ultrasound of intensity I0 is incident normally on the boundary between
two media, as shown in Fig. 5.1.

specific acoustic specific acoustic

impedance Z1 impedance Z2

incident beam transmitted beam

intensity I0 intensity IT

Fig. 5.1

The media have specific acoustic impedances Z1 and Z2.

The intensity of the ultrasound beam transmitted across the boundary is IT.

Explain the significance of the magnitudes of Z1 and of Z2 on the ratio IT / I0.

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

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

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

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

[Total: 6]

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6 Two solid metal spheres A and B, each of radius 1.5 cm, are situated in a vacuum. Their centres
are separated by a distance of 20.0 cm, as shown in Fig. 6.1.

1.5 cm 1.5 cm
20.0 cm

sphere A sphere B

Fig. 6.1 (not to scale)

Both spheres are positively charged.

Point P lies on the line joining the centres of the two spheres, at a distance x from the centre of
sphere A.

The variation with distance x of the electric field strength E at point P is shown in Fig. 6.2.

50

40

30

E / N C–1
20

10

0
0 2 4 6 8 10 12 14 16 18 20
–10 x / cm

–20

–30

–40

–50

Fig. 6.2

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(a) Use Fig. 6.2 to determine the ratio

magnitude of charge on sphere A
.
magnitude of charge on sphere B
Explain your working.

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

(b) The variation with distance x of the electric potential V at point P is shown in Fig. 6.3.

0.8

0.7

0.6
V/V
0.5

0.4

0.3

0.2

0.1

0
0 2 4 6 8 10 12 14 16 18 20
x / cm

Fig. 6.3

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An α-particle is initially at rest on the surface of sphere A.

The α-particle moves along the line joining the centres of the two spheres.

Determine, for the α-particle as it moves between the two spheres,

(i) its maximum speed,

maximum speed = ................................................. m s–1 [3]

(ii) its speed on reaching the surface of sphere B.

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

[Total: 8]

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7 (a) (i) Define capacitance.

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

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

(ii) Use the expression for the electric potential due to a point charge to show that an isolated
metal sphere of diameter 25 cm has a capacitance of 1.4 × 10–11 F.

[2]

(b) Three capacitors of capacitances 2.0 μF, 3.0 μF and 4.0 μF are connected as shown in Fig. 7.1
to a battery of e.m.f. 9.0 V.

4.0 μF

3.0 μF

2.0 μF

9.0 V

Fig. 7.1

Determine

(i) the combined capacitance of the three capacitors,

capacitance = ..................................................... μF [1]

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(ii) the potential difference across the capacitor of capacitance 3.0 μF,

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

(iii) the positive charge stored on the capacitor of capacitance 2.0 μF.

charge = .................................................... μC [2]

[Total: 8]

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8 A circuit incorporating an ideal operational amplifier (op-amp) is shown in Fig. 8.1.

50 kΩ
RA
+9 V
100 Ω
–
RB

10 kΩ +
VIN
–9 V V

Fig. 8.1

The supply to the op-amp is +9 V / –9 V.

The output of the amplifier is measured using a voltmeter having a range 0 – 5.0 V.

A switch enables the inverting input to the op-amp to be connected to either resistor RA or
resistor RB.

(a) A positive potential +VIN is applied to the input to the circuit.

On Fig. 8.1, mark with the letter P the positive connection of the voltmeter such that the
voltmeter shows a positive reading. [1]

(b) Calculate the potential VIN such that the voltmeter has a full-scale deflection when the
inverting input to the op-amp is connected to

(i) resistor RA of resistance 100 Ω,

VIN = ...................................................... V [2]

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(ii) resistor RB of resistance 10 kΩ.

VIN = ...................................................... V [1]

(c) Suggest a use for this type of circuit.

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

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

[Total: 5]

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9 A stiff wire is held horizontally between the poles of a magnet, as illustrated in Fig. 9.1.

stiff
wire

Fig. 9.1

When a constant current of 6.0 A is passed through the wire, there is an additional downwards
force on the magnet of 0.080 N.

(a) On Fig. 9.1, draw an arrow on the wire to show the direction of the current in the wire.
Explain your answer.

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

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

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

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

(b) The constant current of 6.0 A is now replaced by a low-frequency sinusoidal current.
The root-mean-square (r.m.s.) value of this current is 2.5 A.

Calculate the difference between the maximum and the minimum forces now acting on the
magnet.

difference = ...................................................... N [4]

[Total: 7]
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10 Explain the function of the non-uniform magnetic field that is superimposed on a large uniform
magnetic field in diagnosis using nuclear magnetic resonance imaging (NMRI).

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

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

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

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

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

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

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

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

[Total: 4]

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11 (a) State Faraday’s law of electromagnetic induction.

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

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

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

(b) An alternating current is passed through an air-cored solenoid.

An iron core is inserted into the solenoid and then held stationary within the solenoid. The
current in the solenoid is now smaller.

Explain why the root-mean-square (r.m.s.) value of the current in the solenoid is reduced as a
result of inserting the core.

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

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

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

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

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

(c) Practical transformers are very efficient. However, there are some power losses.

State two sources of power loss within a transformer.

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

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

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

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

[Total: 7]

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12 (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 isolated atom are shown in Fig. 12.1.

–0.54 eV
–0.85 eV

energy
–1.51 eV

–3.40 eV

Fig. 12.1

For the emission spectrum associated with these energy levels,

(i) on Fig. 12.1, mark with an arrow the transition that gives rise to the shortest wavelength,
[1]

(ii) show that the wavelength of the transition in (i) is 4.35 × 10–7 m.

[2]

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(c) (i) State what is meant by the de Broglie wavelength.

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

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

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

(ii) Calculate the speed of an electron having a de Broglie wavelength equal to the
wavelength in (b)(ii).

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

[Total: 9]

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13 Outline the principles of computed tomography (CT scanning).

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

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

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

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

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

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

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

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

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

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

[Total: 6]

14 Phosphorus-30 ( 30
15 P) was the first artificial radioactive nuclide to be produced in a laboratory. This
was achieved by bombarding aluminium-27 ( 27 13Al) with α-particles.

A partial nuclear equation to represent this reaction is

27
13Al + α → 30
15 P + Φ

(a) State the full nuclear notation for

(i) the α-particle,

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

(ii) the particle represented by the symbol Φ.

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

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(b) Data for the rest masses of the particles in the reaction are given in Fig. 14.1.

particle mass / u
27 26.98153
13Al

α 4.00260
30
15 P
29.97830

Φ 1.00867

Fig. 14.1
Calculate, for this reaction,

(i) the change in the total rest mass of the particles,

mass change = ....................................................... u [2]

(ii) the energy, in joule, equivalent to the mass change calculated in (i).

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

(c) With reference to your answer in (b)(i), comment on the energy of the α-particle such that the
reaction can take place.

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

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

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

...............................................................................................................................................[2]
[Total: 8]

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