Download s040211-examII

THE INCREDIBLE COLLEGE
PHYSICS A-LEVEL PAPER II
Time allowed : 3 hours
This paper must be answered in English.
SECTION A - Multiple-choice Questions - Answer ALL Questions
SECTION B
- Answer Any THREE Questions
INSTRUCTIONS FOR SECTION A
1. All the answers should be marked on the Answer Sheet.
2. Note that you may only mark ONE answer to each question. Two or more answers will
score NO MARKS.
3. All questions carry equal marks. No marks will be deducted for wrong answers.
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Useful Formulae in Advanced Level Physics
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SECTION A
There are 45 questions in this section. Answer ALL questions. Each question is followed by
five suggested answers. Select the best answer in each case. You should spend 1 hour and 45
minutes on this section. Where necessary, take g to be 10 m s2 and take c to be 3  108 m s1.
1. The graph below shows the time variation
of a net force, F, acting on an object of
mass 2 kg. The object is initially at rest
and then moves along a straight line.
Which of the following statements is/are
correct ?
F/N
2. (Continued)
B.
E
5
s
t/s
C.
E
4
(1) The object is accelerating in the first 4
seconds.
(2) The final momentum of the object is
greater than 10 kg m s-1
(3) The maximum speed of the object is
greater than 5 m s-1.
A.
B.
C.
D.
E.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
s
D.
E
2. A block slides from rest down an inclined
plane. The frictional force between the
block and the plane is constant. Which
one of the following graphs best shows
the variation of E, the sum of kinetic and
potential energy of the block, with the
distance travelled, s?
s
E.
E
A.
E
s
s
-3-
3. Two identical balls, A and B, each
suspended by a light inextensible string
of length l to a common point X. A is
raised and then released through an angle
of 60o as shown. The collision between A
and B is perfectly elastic. What are the
speed of A and the speed of B, just after
the collision?
X
l
4. (Continued)
(1) The speed of the ball B on leaving the
toy gun.
(2) The vertical height of the target above
the ball.
(3) The horizontal distance of the ball
from the target.
A.
B.
C.
D.
E.
60o
l
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
A
5. The figure shows the vertical transverse
cross-section of a frictionless circular
track which banks at angle  with the
horizontal. The radius of the track is r.
When a car is moving along the track,
which of the followings about the car
is/are correct?
B
Speed of A
A.
0
B.
0
Speed of B
gl
2
gl
gl
2
gl
2
gl
C.
D.
E.
gl
2
0
gl
4. A ball B is aimed to shoot at the target
held by an electromagnet by adjusting the
angle  between the barrel of the toy gun
and the horizontal as shown. The target
will be released at the same time when B
leaves the barrel of the toy gun. Which
of the following factors determine(s) the
value of ?
IX > IY > IZ IX > IY > IZ
target
(1) There is only one speed v that the car
can drive without skidding.
(2) If the car is moving at a speed higher
than v , the car will skid up the slope.
(3) If the car carries more passengers, it
can move at a speed higher than v
without skidding.
A.
B.
C.
D.
E.
B

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(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
6. A stationary uranium nucleus of mass 238
units disintegrates by emitting an
alpha-article. The mass of the resulting
nucleus has a mass of 234 units. What
percentage of the total kinetic energy
generated in the decay of uranium-238
will be carried away by the
alpha-particle?
A. 1 %
B. 13 %
C. 47 %
D. 82 %
E. 98 %
9. (Continued)
Its moment of inertia about the x, y and z
axes are Ix, Iy and Iz respectively. (Given :
m1 = 1 kg, m2 = 2 kg and m3 = 3 kg)
y
m3
z
7. An object connected to a spring vibrates
horizontally on a smooth surface with a
period of 2.0 s. It is set into simple
harmonic motion by releasing it from
maximum displacement A, measured
from the right to the centre of motion.
After what time will the object be at a
displacement A/4 measured to left from
the centre of motion?
A.
B.
C.
D.
E.
x
m3
Arrange Ix, Iy and Iz in ascending order.
A.
B.
C.
D.
E.
Ix < Iy < Iz
Ix < Iz < Iy
Iy < Ix < Iz
Iy < Iz < Ix
Iz < Ix < Iy
10. Two isolated point charges +Q and q,
separated by r in vacuum, attract each
other with a force F. If they are moved
apart a further distance r, then the new
force between them and the work done
required are respectively
0.08 s
0.13 s
0.42 s
0.58 s
0.66 s
8. When a body performs simple harmonic
motion, which of the following is/are /2
radian out of phase with the
displacement?
(1) impulse
(2) velocity
(3) acceleration
A.
B.
C.
D.
E.
m1
m2
A.
B.
C.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
D.
E.
9. Four masses are attached to a light
circular hoop of radius 1 m as shown in
the following diagram. The resulting
configuration is free to rotate about the x,
y and z axes.
Force
F
2
F
2
F
4
F
4
F
4
Work done
Qq
40 r
Qq

80 r
Qq
40 r
Qq
80 r
Qq

80 r
11. Equal currents flow through two uniform
copper wires; one of which has a
diameter half of the other. The ratio of the
drift velocity of electrons in the thin wire
to that in the thick wire is
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11. (Continued)
A. 4 : 1
B. 2 : 1
C. 1 : 1
D. 1 : 2
E. 1 : 4
14. (Continued)
A. 0.2 V
B. 0.4 V
C. 0.6 V
D. 0.8 V
E. 1.0 V
12. A source of e.m.f  and internal resistance
r is connected to an external resistor of
resistance R. When R = r,
(1) the total power supplied by the source
is maximum.
(2) the source is operating at its
maximum efficiency.
(3) the source is delivering the maximum
power to the external resistor.
15. Two parallel straight conductors,
separated by a distance r, carry the same
current in the opposite direction. Which
of the following statements is/are
correct?
(1) The two wires repel each other.
(2) The force acting on each wire is
inversely proportional to r.
(3) The wires produce a magnetic field
with minimum flux density midway
between them.
A.
B.
C.
D.
E.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
13. A parallel-plate capacitor of capacitance
C is formed by two rectangular metal
plates having separation d. Now each of
the plates is cut into two smaller identical
ones to form two capacitors, each with
d
plate separation
. What is the
2
capacitance when they are connected in
series?
A.
B.
C.
D.
E.
1
C
8
1
C
4
1
C
2
C
2C
14. An uncharged capacitor C of capacitance
1000 pF is connected in parallel with a
charged capacitor C1 of capacitance
250 pF which is initially charged to a p.d.
of 2 V. The final p.d. across the
capacitors is
A.
B.
C.
D.
E.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
16. Which of the following statements about
the use of a Hall probe in measuring the
magnetic flux density of a magnetic field
is/are true?
(1) The plane of the semiconducting slice
inside a Hall probe should be in
parallel with the magnetic field.
(2) A Hall probe can only be used for
measuring the magnetic flux density
of a steady magnetic field.
(3) A Hall probe can be used for
comparing the directions of two
magnetic fields.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1), (2) and (3)
17. The coil of galvanometer is suspended at
the end of a fibre and is wound on a light
former. Which of the following factors
will increase current sensitivity of the
galvanometer?
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17. (Continued)
19. A coil of inductance 4.0 H is connected in
series with a switch S and a cell of e.m.f.
12 V. The total resistance of the circuit is
3.0 . What are the initial rate of growth
of the current when the switch is closed
and the final steady value of current in the
circuit?
(1) Replace the fibre with a weaker one
which has a smaller torsional
constant.
(2) Increase the number of turns of the
coil.
(3) Use a stronger magnet.
Initial rate of
growth
A. 0 A s 1
B. 0 A s
A.
B.
C.
D.
E.
C. 3 A s 1
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
D. 3 A s
E. 4 A s
18. A solenoid is connected to an a.c. supply.
A search coil is placed at the centre of the
solenoid, with their axes parallel to one
another. If the frequency of the a.c.
supply is doubled and the amplitude of
the current is halved, which of the
following statements is/are true?
(1) The magnetic flux density inside the
solenoid is halved.
(2) The maximum rate of change of
magnetic flux through the search coil
is unchanged.
(3) The frequency of the induced e.m.f. in
the search coil is doubled.
A.
B.
C.
D.
E.
1
1
1
Final steady
value
3A
4A
3A
4A
3A
20. A d.c. motor is connected to a battery of
15 V. If the efficiency of the motor is
80 % at steady state, what is the back
e.m.f.?
A.
B.
C.
D.
E.
3V
6V
9V
12 V
15 V
21. Which of the following devices make(s)
use of eddy currents?
(1) Induction furnace
(2) Electromagnetic
damping
in
galvanometers
(3) Motor car speedometer
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
A.
B.
C.
D.
E.
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(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
22. A 120 Vrms, 40 W bulb is connected in
series with a capacitor and a 220 Vrms, 50
Hz mains. If the bulb is in its normal
operation, the capacitance of the
capacitor is
A.
B.
C.
D.
E.
24. (Continued)
R
1.06 F
4.82 F
5.75 F
8.84 F
9.63 F
P
23. The circuit shows a npn transistor and
two resistors connected to a 6 V d.c.
power supply. The current gain of the
transistor is 150. At this setting, the
base-emitter voltage is VBE  0.7 V , the
collector-emitter voltage VCE  3.0 V
and the collector current is I C  3 mA .
What must be the values of the load
resistor RL and the base resistor RB?
(1) Decreasing the temperature.
(2) Increasing R.
(3) Moving the pointer P upwards.
A.
B.
C.
D.
E.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
25. What kind(s) of mechanical waves can be
transmitted through gases and solids?
A.
B.
C.
A.
B.
C.
D.
E.
RL
2 k
2 k
1 k
1 k
1 k
D.
RB
265 k
300 k
265 k
300 k
325 k
E.
24. In the circuit below, the LED is ON.
Which of the following changes could
turn it OFF?
Gaseous medium
longitudinal
wave only
longitudinal
wave only
transverse wave
only
transverse wave
only
longitudinal and
transverse waves
Solid medium
longitudinal
wave only
longitudinal and
transverse waves
transverse wave
only
longitudinal and
transverse waves
longitudinal and
transverse waves
26. A plane progressive wave is represented
by the equation
y = 10 sin (500t  20x)
where y is the displacement in
millimetres, t is in seconds and x is the
distance in metres measured from a fixed
origin. The speed of the wave is
-8-
26. (Continued)
A. 10 ms1
B. 20 ms1
C. 25 ms1
D. 500 ms1
E. 104 ms1
28. (Continued)
(1) y(t) = y1(t) + y2(t)
(2) A = A1 + A2
(3) I = I1 + I2
27. An unpolarized light is incident at an
angle other than the Brewster angle as
shown below. An observer uses a
polaroid to analyse the reflected light.
When he rotates the polaroid slowly,
which of the following about the light
intensity is/are correct?
(1) The light intensity is constant.
(2) The light intensity is zero at certain
moment.
(3) The light intensity varies between
maximum and minimum values.
A.
B.
C.
D.
E.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
28. S1 and S2 are two sound sources and P is a
point such that D >> a. At point P the
displacements of the waves from S1 and
S2 are denoted by y1(t), and y2(t), the
amplitudes by A1 and A2 and the
intensities by I1 and I2. Also let y(t), A and
I denote the corresponding quantities of
the resultant wave at P. Which of the
following statements is/are in general
true?
A.
B.
C.
D.
E.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
29. A monochromatic light is incident
normally on a grating and the first order
image is observed at  = 10. What is the
highest order of image that can be
observed?
A. 2
B. 3
C. 4
D. 5
E. 6
30. The electromagnetic spectrum can be
classified as different types of radiation.
Which of the following statements
correctly describe(s) the radiations?
(1) Each radiation has well defined
cut-off frequencies or wavelengths
distinguishing
it
from
other
radiations.
(2) The distinction of one radiation from
another is determined by how the
radiation is detected.
(3) The distinction of one radiation from
another is determined by how the
radiation is produced.
A.
B.
C.
D.
E.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
31. When a sound wave passes through air,
an oscillatory motion is added to the
normal random motion of the air
molecules.
-9-
31. (Continued)
Which of the following diagrams best
represents the actual oscillatory motion of
the air molecules, in both magnitude and
direction, at different points in a closed
air column vibrating in its fundamental
mode?
32. A truck carrying an observer and a sound
source is moving with velocity of 30 ms1
towards a stationary reflecting surface.
The apparent frequency received by the
observer is f. If the truck is moving away
from the surface at 30 ms1, the apparent
frequency is f. Assuming the velocity of
sound to be 330 ms1, find the ratio f/f.
A. 1
B. 1.2
C. 1.44
D. 2.4
E. 2.88
33. (Continued)
34. The angular magnification of an
astronomical telescope is 10 when in
normal adjustment. A beam of light
parallel to the axis of the telescope is
incident on the objective which has a
diameter of 100 mm. If all the light
entering the objective is collected by the
eyepiece, what is the minimum diameter
of the eyepiece?
A.
B.
C.
D.
E.
35.
33. Let  be the intensity level at a point
which is at a distance r from a sound
source of power P. Assuming that the
source emits sound uniformly in all
directions, how will  vary with log10r?
- 10 -
2 mm
5 mm
10 mm
20 mm
100 mm
35. (Continued)
A liquid is flowing in a pipe as shown
above. The cross-sectional areas at ‘a’
and at ‘b’ are A and 3A respectively and
the velocities at 'a' is 4 ms1. If the
pressure at ‘a’ and ‘b’ are equal, calculate
the difference in levels h.
A. 0.35
B. 0.53
C. 0.71
D. 0.80
E. 1.06
37. (Continued)
36. An ideal gas is taken through the series of
changes shown.
A. DA represents an isobaric expansion
B. The work done by the gas during the
change AB is equal to that done on
the gas during the change CD
C. No work is done on the gas during the
change DA.
D. No work is done on the gas during the
change CD.
E. No net work is done by the gas in
completing one cycle.
38. A steel bar has a radius of r1 for half of its
1
length and a radius of r2 = r1 for the
2
other half. When subject to axial loading,
what is the ratio of the extension l1 : l2
of the two halves?
A. 1:2
B. 1:4
C. 4:1
D. 2:1
E. 2 :1
39. The graph below shows the variation of
the interatomic force F with the
interatomic distance r. When F = F, what
is the strain?
37. An ideal gas is heated at constant
pressure. Which of the following graphs
best represents the variation of the
internal energy per unit volume of the gas
with temperature ?
- 11 -
39. (Continued)
A.
B.
C.
D.
E.
40. (Continued)
r0r
r / r0
(r  r0) / r0
(r  r0) / r
(r0 / r)2
40. The voltage variation of two supplies Vx
and Vy with time are shown below. They
are applied to the x-plates and y-plates of
a CRO respectively.
41.
Which of the following best represents
the trace on the screen?
- 12 -
The diagram shows five electron energy
levels of a hydrogen atom. Which of the
following statements is/are correct?
(1) The atom is most stable when the
electron has zero energy.
(2) When the electron is in the 13.6 eV
level, the atom can absorb 10.2 eV
from a colliding electron.
(3) When the electron is in the 1.5 eV
level, the atom can emit a photon of
energy 1.9 eV.
41. (Continued)
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1), (2) and (3)
43. Polonium 214 may decay into polonium
210 by emitting an  particle followed by
42. In the investigation of the structure of the
atom of a particular element, a scientist
suggests the existence of four energy
levels as shown below. E1 is the lowest
energy, E4 is the highest. He proposes
five possible energy transitions as shown
below by the arrows.
A.
B.
C.
D.
E.
44. An isotope has a half-life of 8 years. After
a period of 64 years, the fraction of the
isotope remaining is
A.
B.
C.
D.
E.
Which one of the spectra below most
closely corresponds to the suggested
transitions?
a  particle and a  ray
two  particles
an  particle and a  particle
two  rays
a  ray
1/4
1/8
1/64
1/128
1/256
45. Which of the following phenomena of an
atom can be explain by Rutterford’s
model of an atom?
(1) Most of the space outside the nucleus
of an atom is empty.
(2) The characteristic spectrum of an
atom.
(3) Electrons orbiting around the nucleus
of an atom do not radiate
electromagnetic waves.
A.
B.
C.
D.
E.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
END OF SECTION A
- 13 -
SECTION B
Answer any THREE questions from this section.
Write your answers in the ANSWER
BOOK provided. You should spend 1 hour and 15 minutes on this section.
1. (a) State Newton's laws of motion.
(3 marks)
(b) State the principle of conservation of linear momentum and show that it can be derived
from Newton’s laws of motion.
(3 marks)
(c) An object placed on a turntable may curve outwards to the edge if the turntable rotates
at a high speed. A student says that there is a force acting on the object to push it
outward. Comment on the student's argument with the aid of a diagram.
(3 marks)
(d) Consider a solid cylinder of uniform density, mass M and radius r rolls down a rough
inclined plane without slipping as shown below. The moment of inertia of the solid
cylinder about the axis through its centre of mass and perpendicular to the plane of
1
rotation is I  Mr 2 .
2

(i)
A student says that the rolling of the solid cylinder is a combined motion of a pure
translational motion and a pure rotational motion. Justify the statement. Write
also equations to show the forces and torque acting on the solid cylinder. (Hint :
Consider the torque by the frictional force on the solid cylinder about its centre of
mass)
(ii) Hence derive an expression for the linear acceleration of the solid cylinder in terms
of M, r, g and  from (d)(i).
(iii) Determine whether a similar hollow cylinder of the same mass M and radius r will
roll down the inclined plane at a greater or smaller acceleration. Explain briefly.
(7 marks)
2. A d.c. motor, as shown below, is designed in such a way that the field coil is connected to its
armature in parallel. The motor runs at a steady angular velocity  when a current I flows
through the armature.
- 14 -
2. (Continued)
Some information about the motor are listed as follows:
 Number of turns of the coil in the armature is N.
 The area of the coil in the armature is A.
 The resistance of the coil in the armature is R.
 The magnetic field applied to the armature is B.
 The voltage supplied to the motor is V.
(a) Explain briefly the fundamental operation of this motor.
(3 marks)
(b) (i) Draw a diagram to show the position of the coil in the magnetic field at which the
coil is subjected to the maximum torque.
(ii) Derive an expression for the maximum torque in terms of N, B, I and A from the
first principle.
(4 marks)
(c) What is the maximum induced e.m.f. in the coil? Express it in terms of , B, A and N.
(1 mark)
(d) From the above results, give an account of what will happen in each of the following
situations.
(i) A greater load is driven by the motor.
(ii) The direction of the current flow in the circuit is reversed.
(iii) A resistor is connected in series with the field coil.
(8 marks)
3. (a) (i)
(1) Explain the difference between plane polarized light and unpolarized light.
Give one example of each of them.
(2) Describe how one can use a piece of polaroid to test whether a beam of light is
plane polarized or not.
(ii) When a beam of unpolarized light is incident onto a piece of glass or a thin layer of
water, the reflected light is usually described as partially polarized.
(1) What is the meaning of the term partially polarized ?
(2) With the aid of an appropriate diagram, deduce an expression for the angle of
incidence at which the reflected light becomes plane polarized. Show your
steps clearly.
(9 marks)
- 15 -
3. (Continued)
(b) (i) (1) Explain the meaning of the term red shift.
(2) Explain why red shift provides an evidence for the expanding universe.
(ii) Since the sun rotates about an axis passing through its centre, the wavelengths of
light waves emitted from it differ at both ends of the diameter. Use Doppler effect
to explain, quantitatively, how the rotational speed of the sun can be found by the
above observations.
(7 marks)
4. (a) Suppose that there are N molecules of an ideal gas, each of mass m, inside a spherical
container of radius r. The diagram below shows the path of one of the gas molecules
travelling with speed c1 and rebounding elastically from the container wall at points P,
Q and R.
F (force perpendicular to A)
(i)
By considering there are N1 molecules with speed c1, N2 molecules with speed c2,
etc and using the above model, show that the total pressure P exerted by the gas on
the container wall is given by the expression
1
PV  Nmc 2
3
where V is the volume of the container and c 2 is the mean square speed of the gas.
State your assumptions.
(ii) Hence, express the average kinetic energy of each gas molecule in terms of the
absolute temperature T.
(8 marks)
(b) The ideal gas equation PV  nRT is usually modified by the Van der Waals' equation
a
a
(P 
)(V  b)  nRT for a real gas. Account for the terms ( P  2 ) and (V  b)
V
V2
where a and b are constants.
(5 marks)
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4. (Continued)
(c) The graph below relates the pressure and volume of a fixed mass of an ideal gas that is
compressed isothermally from A to B.
Pressure
B
A
Volume
Using the first law of thermodynamics, state and explain whether there is heat transfer
to or from the gas and work is done on or by the gas.
(3 marks)
5. (a) Draw the experimental set-up for investigating the collisions of moving electrons with
gaseous mercury atoms. Discuss the importance of the results.
(4 marks)
(b) (i) With the aid of diagrams, briefly describe and explain the characteristics of the
hydrogen spectrum and the X-ray spectrum. Why do the lines in the X-ray
spectrum have much shorter wavelengths?
(ii) Explain why dark lines are observed in the Sun’s spectrum.
(9 marks)
(c) (i) What is meant by the word LASER ?
(ii) List TWO properties that make LASER a suitable source for study of interference
and diffraction phenomena.
(iii) Suggest TWO practical applications of LASER in daily life.
(3 marks)
END OF SECTION B
END OF PAPER
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