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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education
Advanced Subsidiary Level and Advanced Level
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The number of marks is given in brackets [ ] at the end of each question or
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PHYSICS 9702/21
Paper 2 AS Structured Questions May/June 2010
1 hour
Candidates answer on the Question Paper.
No Additional Materials are required.
For Examiner’s Use
1
2
3
4
5
6
7
Total
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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 + 12at 2
v2 = u2 + 2as
work done on/by a gas, W = p�V
gravitational potential, φ = – Gm
r
hydrostatic pressure, p = ρgh
pressure of an ideal gas, p = 13
Nm
V
simple harmonic motion, a = – ω 2x
velocity of particle in s.h.m., v = v0 cos ωt
v = ± ω (x02 – x 2)
electric potential, V = Q4πε0r
capacitors in series, 1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel, C = C1 + C2 + . . .
energy of charged capacitor, W = 12
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 1
2
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For
Examiner’s
Use
Answer all the questions in the spaces provided.
1 A unit is often expressed with a prefix. For example, the gram may be written with the prefix
‘kilo’ as the kilogram. The prefix represents a power-of-ten. In this case, the power-of-ten
is 103.
Complete Fig. 1.1 to show each prefix with its symbol and power-of-ten.
prefix symbol power-of-ten
kilo
nano
centi
................................
................................
k
n
.......................
M
T
103
.............................
10–2
106
1012
Fig. 1.1
[4]
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For
Examiner’s
Use
2 (a) Complete Fig. 2.1 to show whether each of the quantities listed is a vector or a scalar.
vector / scalar
distance moved
speed
acceleration
................................
................................
................................
Fig. 2.1
[3]
(b) A ball falls vertically in air from rest. The variation with time t of the distance d moved by
the ball is shown in Fig. 2.2.
0
0
1
2
3
4
5
0.2 0.4 0.6
t /s
d /m
0.8 1.0 1.2
Fig. 2.2
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For
Examiner’s
Use
(i) By reference to Fig. 2.2, explain how it can be deduced that
1. the ball is initially at rest,
..................................................................................................................................
..................................................................................................................................
.............................................................................................................................. [2]
2. air resistance is not negligible.
..................................................................................................................................
.............................................................................................................................. [1]
(ii) Use Fig. 2.2 to determine the speed of the ball at a time of 0.40 s after it has been
released.
speed = ....................................... m s–1 [2]
(iii) On Fig. 2.2, sketch a graph to show the variation with time t of the distance d moved
by the ball for negligible air resistance. You are not expected to carry out any further
calculations. [3]
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3 (a) The variation with extension x of the tension F in a spring is shown in Fig. 3.1.
0
0
50
100
150
200
1.0 2.0 3.0
x /cm
F /N
4.0
Fig. 3.1
Use Fig. 3.1 to calculate the energy stored in the spring for an extension of 4.0 cm.
Explain your working.
energy = .............................................. J [3]
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(b) The spring in (a) is used to join together two frictionless trolleys A and B of mass M1 and
M2 respectively, as shown in Fig. 3.2.
spring
trolley A
mass M1
trolley B
mass M2
Fig. 3.2
The trolleys rest on a horizontal surface and are held apart so that the spring is
extended.
The trolleys are then released.
(i) Explain why, as the extension of the spring is reduced, the momentum of trolley A
is equal in magnitude but opposite in direction to the momentum of trolley B.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
.............................................................................................................................. [2]
(ii) At the instant when the extension of the spring is zero, trolley A has speed V1 and
trolley B has speed V2.
Write down
1. an equation, based on momentum, to relate V1 and V2,
..................................................................................................................................
.............................................................................................................................. [1]
2. an equation to relate the initial energy E stored in the spring to the final
energies of the trolleys.
..................................................................................................................................
.............................................................................................................................. [1]
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(iii) 1. Show that the kinetic energy EK of an object of mass m is related to its
momentum p by the expression
EK =
p2
2m
.
[1]
2. Trolley A has a larger mass than trolley B.
Use your answer in (ii) part 1 to deduce which trolley, A or B, has the larger
kinetic energy at the instant when the extension of the spring is zero.
..................................................................................................................................
.............................................................................................................................. [1]
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4 (a) State what is meant by the diffraction of a wave.
..........................................................................................................................................
..........................................................................................................................................
...................................................................................................................................... [2]
(b) A laser produces a narrow beam of coherent light of wavelength 632 nm. The beam is
incident normally on a diffraction grating, as shown in Fig. 4.1.
165 cm screen
Y
P 76 cm
diffraction
grating
laser light
wavelength 632 nm
X
Fig. 4.1
Spots of light are observed on a screen placed parallel to the grating. The distance
between the grating and the screen is 165 cm.
The brightest spot is P. The spots formed closest to P and on each side of P are X
and Y.
X and Y are separated by a distance of 76 cm.
Calculate the number of lines per metre on the grating.
number per metre = ................................................. [4]
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(c) The grating in (b) is now rotated about an axis parallel to the incident laser beam, as
shown in Fig. 4.2.
laser
light
diffraction
grating
before rotation
laser
light
diffraction
grating
after rotation
Fig. 4.2
State what effect, if any, this rotation will have on the positions of the spots P, X and Y.
..........................................................................................................................................
..........................................................................................................................................
..........................................................................................................................................
...................................................................................................................................... [2]
(d) In another experiment using the apparatus in (b), a student notices that the distances
XP and PY, as shown in Fig. 4.1, are not equal.
Suggest a reason for this difference.
..........................................................................................................................................
...................................................................................................................................... [1]
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5 (a) State what is meant by an electric field.
..........................................................................................................................................
...................................................................................................................................... [1]
(b) The electric field between an earthed metal plate and two charged metal spheres is
illustrated in Fig. 5.1.
earthed
metal plate
charged
sphere
charged
sphere
Fig. 5.1
(i) On Fig. 5.1, label each sphere with (+) or (–) to show its charge. [1]
(ii) On Fig. 5.1, mark a region where the magnitude of the electric field is
1. constant (label this region C), [1]
2. decreasing (label this region D). [1]
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(c) A molecule has its centre P of positive charge situated a distance of 2.8 × 10–10 m from
its centre N of negative charge, as illustrated in Fig. 5.2.
P
N
30°
applied
electric field
5.0 × 104 V m–1
molecule
2.8 × 10–10 m
Fig. 5.2
The molecule is situated in a uniform electric field of field strength 5.0 × 104 V m–1. The
axis NP of the molecule is at an angle of 30° to this uniform applied electric field.
The magnitude of the charge at P and at N is 1.6 × 10–19 C.
(i) On Fig. 5.2, draw an arrow at P and an arrow at N to show the directions of the
forces due to the applied electric field at each of these points. [1]
(ii) Calculate the torque on the molecule produced by the forces in (i).
torque = ......................................... N m [2]
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For
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Use
6 An electric heater is to be made from nichrome wire. Nichrome has a resistivity of
1.0 × 10–6 Ω m at the operating temperature of the heater.
The heater is to have a power dissipation of 60 W when the potential difference across its
terminals is 12 V.
(a) For the heater operating at its designed power,
(i) calculate the current,
current = .............................................. A [2]
(ii) show that the resistance of the nichrome wire is 2.4 Ω.
[2]
(b) Calculate the length of nichrome wire of diameter 0.80 mm required for the heater.
length = ............................................. m [3]
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(c) A second heater, also designed to operate from a 12 V supply, is constructed using the
same nichrome wire but using half the length of that calculated in (b).
Explain quantitatively the effect of this change in length of wire on the power of the
heater.
..........................................................................................................................................
..........................................................................................................................................
..........................................................................................................................................
...................................................................................................................................... [3]
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Use
7 One of the isotopes of uranium is uranium-238 ( 238
92 U).
(a) State what is meant by isotopes.
..........................................................................................................................................
..........................................................................................................................................
...................................................................................................................................... [2]
(b) For a nucleus of uranium-238, state
(i) the number of protons,
number = ................................................. [1]
(ii) the number of neutrons.
number = ................................................. [1]
(c) A uranium-238 nucleus has a radius of 8.9 × 10–15 m.
Calculate, for a uranium-238 nucleus,
(i) its mass,
mass = ............................................ kg [2]
(ii) its mean density.
density = ...................................... kg m–3 [2]
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(d) The density of a lump of uranium is 1.9 × 104 kg m–3.
Using your answer to (c)(ii), suggest what can be inferred about the structure of the
atom.
..........................................................................................................................................
..........................................................................................................................................
...................................................................................................................................... [2]
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University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
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