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St. Joseph’s Anglo-Chinese School
2nd Term Examination 2007/2008
F.6 Physics (ASL) II
Time allowed: 1 hour 50 min.
Answer ALL questions in Section A and ANY 2 questions in Section B.
This paper occupies 52% of the aggregate.
SECTION A (30%)
There are 25 questions in this section. Answer ALL questions.
Where necessary, take the acceleration due to gravity to be 10m s-2 and take the speed of light in air to
be 3 x 10-8ms-1.
The last page of this question paper contains a list of physics formulae.
1
A box moves at a uniform velocity of 2 m s-1 on a frictionless horizontal surface. Sand falls into
the box with negligible speed at a rate of 90 kg per minute. What horizontal force is required to
keep the box moving uniformly at 2 m s-1?
A. 0 N
B. 3 N
C. 6 N
D. 90 N
2
A nucleus originally at rest splits into two fragments of unequal mass. The fragment with smaller
mass has a larger
(1) speed
(2) momentum
(3) kinetic energy
A.
(1) only
B.
(2) only
C.
(1) and (3) only
D.
(2) and (3) only
3
A car of mass m travels into a region where the track is an arc of a vertical circle of radius r. At
the bottom of this arc, the car travels at speed v. At this position the vertical force exerted upwards
by the track on the car is
A. mv2/r.
B. mg.
C. mv2/r – mg.
D. mg + mv2/r.
4
The figure shows a small heavy bob P attached to a fixed point A on the ceiling by a light
inextensible string. The bob is pulled aside with the string taut and then released from rest. Which
of the following descriptions is/are true?
(1) When moving towards the lowest point of its path, the angular speed of the bob is increasing.
(2) The centripetal acceleration of the bob is constant.
(3) When the bob is at the lowest point, the tension in the string equals the centripetal force.
1
5
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
A metre rule is clamped horizontally to the edge of a bench so that most of its length overhangs
and it is free to vibrate in simple harmonic motion. The tip of the rule vibrate with an amplitude of
3.5 cm and a maximum speed of 1.0 m s-1. What is the frequency of vibration of the rule?
A. 3.5 Hz
B. 4.0 Hz
C. 4.5 Hz
D. 5.0 Hz
6
A body hanging on a light spring oscillates vertically between levels X and Z as shown below. Its
static equilibrium position is at level Y.
Which of the following statements is/are correct?
(1) The acceleration of the body is zero when it is at level X
(2) The elastic potential energy of the spring is zero when the body is at level Y.
(3) The net downward force acting on the body is at its maximum when it is at level Z.
A.
7
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
The displacement-time graphs of two oscillating particles P and Q are shown below.
Which of the following phase relations between P and Q is correct?
A.
8.
P leads Q by /2
B.
P leads Q by /4
C.
Q leads P by /2
D.
Q leads P by /4
In Young's double-slit experiment, which of the following combinations of monochromatic light,
the slit-separation and the slit-to-screen distance would produce the widest fringe separation on
the screen?
Monochromatic light
Slit-separation
Slit-to-screen distance
A.
red light
1 mm
2m
B.
red light
2 mm
1m
C.
green light
1 mm
2m
D.
green light
2 mm
2m
2
9.
A glass vessel in the shape of a triangular prism is filled with water, and light is incident normally
on the face XY. If the refractive indices for water and glass are
4
3
and
respectively, total
3
2
internal reflection will occur at the glass-air surface XZ only for sin  greater than
A.
2
3
B.
3
4
C.
8
9
D.
16
27
10.
Stationary wave patterns can be produced on an elastic string using the experimental set-up shown
above by adjusting the frequency f of the vibrator. Which of the following statements concerning
the experiment is/are correct?
(1) Stationary wave patterns can be observed for more than one value of the frequency f .
(2) When the frequency f increases, the number of loops for the stationary wave pattern to be
observed also increases.
(3) For a stationary wave pattern to occur, the length of the string must be equal to an integral
number of wavelengths.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
11. Orange light of wavelength 600 nm (in air) is incident normally from air onto a liquid film whose
refractive index is 1.25. For what minimum value of film thickness will the greatest amount of
light be transmitted through the film?
A.
120 nm
B.
240 nm
C.
300 nm
D.
480 nm
12. When monochromatic light is incident normally on a wedge-shaped thin film, an interference
pattern may be seen by reflection. Which of the following changes would increase the number of
fringes per unit length as seen by an observer?
(1) increasing the wavelength of the light
(2) increasing the angle of the wedge
(3) increasing the refractive index of the film material
A.
(3) only
B.
(1) and (2) only
C.
3
(2) and (3) only
D.
(1), (2) and (3)
13.
A and B are two identical containers connected by a tap S initially closed. A contains an ideal gas
at a pressure P1 and a temperature T1. B contains the same gas at a pressure P2 and a temperature
T2. The tap S is then opened. If the temperatures of the containers A and B remain constant at T1
and T2 respectively, the final pressure of the gas mixture will be
P1T2  P2T1
P1T1  P2T2
P1  P2
A.
B.
C. P1 + P2
D.
T1  T2
T1  T2
2
14. Two closed vessels X and Y contain equal masses of an ideal gas. X has a greater volume than Y.
When the temperature T changes, which of the following represents the variation of the pressure P
of the gas in each vessel with temperature T?
A.
B.
C.
D.
15. A vessel of volume 1  10-3 m3 contains 0.72 g of an ideal gas at a pressure of 1  105 Pa. The
r.m.s. velocity of the gas molecules is
A. 20 m s-1.
B. 110 m s-1.
C.
340 m s-1.
D. 650 m s-1.
16
Which of the following properties of molecules of an ideal gas is/are the same on the moon as on
the earth, if the temperature and volume of the gas are unchanged?
(1) The average momentum change when a molecule of the gas rebound from a wall of the
container.
(2) The average kinetic energy of a molecule of the gas.
(3) The weight of a molecule of the gas.
A.
(1) only
B.
(3) only
C.
4
(1) and (2) only
D.
(2) and (3) only
17. Two different ideal gases, A and B, are contained in two identical vessels. If the ratio of their
absolute temperature and the ratio of the root-mean-square speed of the molecules are respectively
2 : 1 and 3 : 1, the ratio of their molecular mass is
A. 2 : 3
B. 2 : 9
C.
1:6
D.
9 :2
18. An inexpansible vessel contains 1.2 kg of gas at 300 K. What is the mass of gas expelled from the
vessel if it is heated from 300 K to 400 K under constant pressure?
A. 0.25 kg
B. 0.3 kg
C. 0.6 kg
D. 0.75 kg
19. A potential difference V is applied between two large parallel plates, distance s apart. An electron,
mass m, charge -e, starts from rest at the negative plate and travels across the gap to the positive
plate. The time taken is
A.
2s
V
B.
m
2eV
s2
eV
C.
D.
2ms 2
eV
20.
The diagram shows a pattern of electric field lines in which X, Y and Z are points marked on one
of the field lines. It would be correct to say that
(1) X is at a higher potential than Z.
(2) a negative charge placed at Z would accelerate to the left along the tangent to the field line at
Z.
(3) the force exerted on a charge at Y would be greater than if the charge were placed at X.
A. (1) only
B. (1) and (2) only
C. (2) and (3) only
D. (1), (2) and (3)
21.
–Q
+Q
W
X
Z
Y
–Q
q
Three charges +Q, –Q and –Q are fixed at the corners W, X and Y respectively of a square as
shown. A fourth charge, q, is fixed at Z, after which the charge at X experiences a NET
electrostatic force indicated by the arrow. q is equal to
A.
+2Q
B.
+Q
C.
5
2 2Q
D.
 2Q
22. X, Y are two different points in an electric field. A small charged object is released from rest at X.
Which of the following conditions would ensure that the charged object will NOT pass through
Y?
A.
B.
C.
D.
The electric field at Y is zero.
The electric field at Y is stronger than that at X.
The electric field between X and Y is not zero.
The electric potentials at X and Y are equal.
23. A resistance wire is connected across the terminals of a battery. Which of the following statements
is incorrect?
A. Before connection to the battery, the conduction electrons in the wire move randomly.
B. After connection to the battery, an electric field is set up along the length of the wire.
C. The conduction electrons in the wire are accelerated momentarily in the opposite direction
D.
to that of the electric field.
The conduction electrons collide with one another, giving out heat energy.
24. Two cylindrical metal rods, X and Y, are made from the same material and have the same mass.
The length of X is three times that of Y. If currents of 1 A and 2 A pass through X and Y
respectively, the ratio of the power dissipation in X to that in Y is
A. 9 : 4
B 9:2
C 3:4
D. 9 :1
25.
Two cells of negligible internal resistance are connected with two resistors as shown. What is the
potential difference between X and Y?
A. 2.33 V
B. 2.00 V
C. 1.67 V
D. 1.33 V
6
Section B (22%)
Answer any TWO questions from this section. Write your answers in the ANSWER sheet provided.
1
(a) Explain what a simple harmonic motion (s.h.m.) is, and why it is called an isochronous
oscillation.
(2 marks)
(b) A rubber ball is dropped freely from a certain height onto a horizontal floor. It rebounds to
the same height after each bounce. In terms of the force acting, state TWO ways in which the
motion, although periodic, differs from simple harmonic motion.
(4 marks)
(c)
The above figure show a simple harmonic pendulum which consists of a bob suspended by a
light, inextensible string of length L from a fixed point. If the bob is slightly displaced to one
side and then released, it will perform s.h.m. The set-up can be used to measure the
acceleration due to gravity g.
(i)
Which force provides the restoring force for the bob to perform s.h.m.?
(ii) Give TWO reasons why a small spherical heavy bob is usually used in the experiment.
L
(iii) The period of oscillation of the pendulum is given by T  2
. Describe briefly how
g
the gravitational acceleration g can be determined from this experiment using a
graphical method. State TWO precautions that should be taken in this experiment.
(6 marks)
7
2
(a) Explain the meaning of the potential difference between two points in an electric field and
hence state the meaning of the potential at a point in the field.
(3 marks)
(b) Distinguish between electromotive force and potential difference.
(2 marks)
(c) The figure shows a circuit consisting of a cell of e.m.f.  and internal resistance r, and two
uniform resistance wires BC and CD. The two wires are equal in length and are made of the
same material, but the cross-sectional area of BC is double that of CD. The total resistance of
the two wires is R. All other connecting wires are of negligible resistance.
A

r
E
V
B
(i)
C
D
Sketch a graph showing the readings of the voltmeter versus the path length along the
circuit when its flying lead is connected to various points along the path ABCDE.
Indicate on your graph the voltmeter readings at various points in terms of , r and R.
Explain the conversion of electrical potential energy of a charge +q passing through
each section of the complete circuit.
(ii) State and discuss the significance of the order of magnitude of the internal resistance of
a 5 kV E.H.T.
(7 marks)
3
(a) In terms of the kinetic theory model of gases, explain:
(i) what an ideal gas is,
(ii) how gases exert pressure on the walls of their containers,
(iii) why compressing a gas increases its temperature.
(7 marks)
(b) The equation of state and kinetic theory equation of an ideal gas can be written as
pV  nRT and pV 
1
Nmc 2 .
3
Two identical vessels containing hydrogen and oxygen respectively are at the same
temperature and pressure. What can you say about the number of molecules, the average
molecular kinetic energy and the mean square speed of the molecules in the two vessels?
Explain briefly. (Assume that the gases behave ideally)
(5 marks)
END OF PAPER
8
Useful Formulae in Advanced Supplementary Level Physics
A1.
v2
a  ω2 r
r
centripetal acceleration
A2.
a  ω 2 x
simple harmonic motion
B1.
d
B2.
d sin   n
C1.
E
C2.
V
C3.
E
V
d
electric field between parallel-plates (numerically)
C4.
C
Q 0 A

V d
capacitance of a parallel plate capacitor
C5.
E
C6.
R
C7.
F  BQv sin 
force on a moving charge in a magnetic field
C8.
F  BIl sin 
force on a current carrying conductor in a magnetic field
C9.
B
C10.
B
C11.
F
D
a
Q
40 r 2
Q
4 0 r
1
CV 2
2
l
A
0 I
2r
 0 NI
l
 0 I1 I 2
2r
fringe width in double slit interference
diffraction grating equation
electric field due to a point charge
electric potential due to a point charge
energy stored in a capacitor
resistance and resistivity
magnetic field due to a long straight wire
magnetic field inside long solenoid
force per unit length between long parallel straight current
carrying conductors
C12.
T  BANI sin 
torque on rectangular current carrying coil in uniform
magnetic field
C13.
E  BAN sin t
simple generator e.m.f.
C14.
VS
N
 S
VP N P
ratio of secondary voltage to primary voltage in a
transformer
D1.
pV  nRT  NkT
equation of state for an ideal gas
D2.
1
pV  Nmc 2
3
kinetic theory equation
D3.
Ek 
D4.
N  N 0 e  kt
D5.
t1 
2
3RT 3
 kT
2N A 2
ln 2
k
molecular kinetic energy
law of radioactive decay
half-life and decay constant
9
St. Joseph’s Anglo-Chinese School
2nd Term Examination 2007/2008
F.6 Physics (ASL) II solution
Section A
1
B
11
B
21
C
2
C
12
C
22
D
3
D
13
A
23
D
4
A
14
D
24
A
5
C
15
D
25
A
6
B
16
C
7
B
17
B
8
A
18
B
9
B
19
D
10
C
20
D
10
11
12
¼V
13
Section B
1. (a) A body is said to describe s.h.m. if its acceleration (or the net force on it) is always in
opposite direction and proportional to its displacement from the equilibrium position.
1
Isochronous oscillation - period (or frequency) of an s.h.m. is independent of the amplitude
of oscillation.
1
(b) SHM:
there exists between the two extreme ends an equilibrium position at which
the net force acting on object is zero.
1
Bouncing ball: no equilibrium position between the two extreme ends and net force is acting.
1
SHM:
the force on the object is always directed towards the equilibrium position. 1
Bouncing ball: the force on the ball is directed towards the centre of the earth except at the
moment of rebound.
1
SHM :
the force on the object is proportional to the displacement from the
equilibrium position.
1
Bouncing ball: the force on the ball is constant except at the moment of rebound.
1
ANY TWO
The (tangential component of the) weight of the bob (i.e. mg sin ) provides the
restoring force.
½
(ii) The centre of mass of the spherical bob can be easily located so that the effective length
L can be measured more accurately.
1
The bob is small/heavy so that the effect due to air resistance is minimized.
1
The bob is heavy so that the mass of the string can be neglected.
1
ANY TWO
(c) (i)
(iii) Measure the period T of the simple pendulum using a stop watch for different values of
L.
1
A graph of T2 against L should be plotted which is a straight line passing through the
origin.
½
Using the formula T  2
L
L
, we have T 2  4 2
g
g
4 2
4 2
Using the slope of the graph =
. Hence g 
.
g
slope
Precautions
½
½
- Ensure the pendulum oscillates with small amplitude (less than 10).
- Make sure the pendulum oscillates on the same vertical plane.
½
½
- In measuring period T, at least 20 oscillations should be counted.
½
ANY TWO
14
2
(a) Potential difference between two points is the work done (or change in p.e.) per unit
positive charge moving from one point to another.
1½
By selecting a reference point (usually the earth or a point at an infinite distance from ½ + ½
any electric charges) in the electric field to be the zero potential, the potential of a point
is taken as the potential difference between that point and the reference point.
½
(b) The electromotive force or e.m.f. of a battery is the energy transferred to unit charge from
chemical energy of the battery when the charge passes through the battery.
1
The potential difference, p.d. or voltage across two points in a circuit is the amount of
electrical energy which changes into other forms of energy when unit positive charge passes
between these points.
1
(c) (i)
Since R 
1
, RBC : RCD  1 : 2
A
VBC : VCD  1 : 2 as the same current

rR
flows through the wires.
1
AB, DE: Since the resistance of the connecting wires are negligible, there is no energy
dissipated as the charge q travels along the connecting wires.
½
BC, CD: When the charge q passes through wires BC and CD, the amount of electrical
potential energy qV (qVBC and qVCD) are changed into heat.
1
 R 
EA: When the charge q passes through the cell, the amount of energy q

rR
(or qVAE) is transferred from the chemical energy of the cell.
(ii) The typical internal resistance of an E.H.T. is of the order of M(106 ) so as to
limit the current it supplies and safety can be ensured.
15
½
½
½
½.
3
(a) (i)
-
An ideal gas is one
for which the molecules have insignificant volumes, i.e. they are effectively points
in the space;
1
in which collisions are the only interactions between molecules, and between
molecules and the walls of the container; (or molecules move freely
without intermolecular forces)
1
in which all collisions are perfectly elastic.
1
(ii) A gas molecule on colliding with a container wall suffers a change of momentum and
hence must be acted on by a force.
1
By Newton’s third law of motion, the container wall must have had a force exerted on it
by the molecule,
½
hence pressure.
½
(iii) Temperature is associated with the average kinetic energy of the molecules in the gas. ½
If the gas is compressed, the wall will be moving inward, a molecule collides with the
wall would therefore rebound with an increased speed, and
1
hence the gas temperature would rise because the average kinetic energy of the
molecules has increased.
½
or (If the gas is compressed, the wall will be moving inward, work is done on the gas
and hence the gas
½
temperature would rise because the average kinetic energy of the molecules has
increased.)
½
(b) According to Avogadro’s law, the gases have the same number of molecules. (As p, V and T
are the same, n is the same according to pV = nRT.)
1
As pV 
1
Nmc 2  nRT
3
3 pV 1
3nRT
 mc 2 
2N
2
2N
1
therefore the average molecular kinetic energy is the same in both cases since T is the same
(or p, V and N are the same).
1
As
1
1
m H c H2  mO cO2
2
2
c H2  cO2
 mH
 mO 
As the molecular mass of hydrogen is smaller than that of oxygen, the mean square speed of
the hydrogen molecules is higher than that of the oxygen
1
molecules since their average molecular kinetic energy is the same.
1
16