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CCC HOH FUK TONG COLLEGE
Second Term Examination, 2004 – 2005
Physics
Secondary : 6S
Time allowed : 3 hrs. ( 8:15 – 11:15 )
Name : _______________________
Date : 28 / 6 / 2005
Max. marks : 107
Class : S.6S
Class. No. : ___
Marks : _____
Instructions
1.
2.
Answer ALL questions in Section A and Section B.
Answer ANY TWO questions in Section C.
3.
Write ALL your answers ( including Multiple Choices ) in the ANSWER BOOK.
In calculations you are advised to show all the main steps in your working.
4.
Assume:
velocity of light in air = 3  108 m s-1
acceleration due to gravity = 10 m s-2
Section A : Structured Questions ( 60 marks )
1. In the sport of bungee jumping, a man steps off a bridge, A, above a river, B, which is 100
m below A. He is attached to the bridge by an elastic cord of unstretched length 60 m.
The cord obeys Hooke’s law. ( Neglect the air resistance, size of the man and the mass of
the cord)
A
100 m
B
i. State Hooke’s law.
( 1 mark )
ii. Calculate the speed of the man at the moment when the cord first becomes taut at
position X.
( 2 marks )
a. The man has a mass of 60 kg and is momentarily brought to rest by the cord when he
reaches the level of the river B. Calculate
i.
the loss of energy by the man as he falls from A to B.
ii.
the elastic energy stored in the cord when the man is at B.
( 2 marks )
b. Find the position Y at which the man attains his maximum speed.
( 3 marks )
c. The motion of the man can be considered as simple harmonic once the cord is
stretched. Sketch a curve to show how the (i) kinetic energy of the man, (ii) elastic
energy stored in the cord, and (iii) gravitational potential energy, of the man changes
with time in the simple harmonic motion.
( Take the river as the reference point of zero gravitational P.E. )
( 3 marks )
2.
Fig.2
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In Fig.2, a diffraction grating is inserted between a light bulb and a translucent screen. Light
rays, after passing through a filter, incident normally onto the grating. Bright fringes are seen
by observers O and O’ behind and in front of the screen respectively. If P is the position of the
third-order bright fringe, the diffraction angle is measured.
By using different wavelengths of light, a table of wavelength  of light and the
corresponding third-order diffraction angle  are tabulated in Table 2.
Wavelength of
447.1
471.3
492.2
501.6
587.6
32.1o
34o
35.8o
36.5o
44.2o
light / nm
Diffraction
angle 
sin 
Table 2
a. Why is the colour filter used ?
( 1 mark )
b. Why is it preferable to make measurements using the third-order instead of the first-order ?
( 2 marks )
c. i. Copy and then complete Table 2. Plot a graph of sin against .
ii. Use the graph to find the grating constant ( i.e. the slit separation ).
( 3 marks )
( 3 marks )
d. If the screen is taken away, explain whether bright fringe pattern can still be observed by
O and O’
( 2 marks )
3. Fig. 3.1 shows a uniform wire, which is held taut but unscratched between a fixed point
and a smooth cylindrical peg of radius 1 cm. The force constant of the wire is 3.84 x 10 3
N m-1. The tension in the wire can be increased by rotating the peg about its fixed axis so
that some wire is wounded onto the peg.
Fig 3.1
a. When the peg is turned through an angle of 2, calculate
i.
the tension in the wire.
( 2 marks )
ii.
the work done in rotating the peg.
( 2 marks )
b. The above wire is a part of a musical instrument. Two knife-edges A and B, are
placed 0.36 m apart under the stretched wire as shown in Fig. 3.2. The mass of the
wire between A and B is 6.4 x 10-4 kg. ( Assume the presence of the two knife-edges
would not affect the tension in the wire. )
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i.
ii.
iii.
Fig 3.2
Calculate the fundamental note emitted when the wire between A and B is
plucked.
( 3 marks )
State THREE difference between the waves in the wire and the
fundamental note emitted.
( 3 marks )
Draw a diagram to show the vibration of the wire between A and B when
it is vibrating at the second harmonics.
( 2 marks )
4. A metal cylinder A of volume 0.5 m3 containing some compressed gas at pressure of 8 x
105 Pa is connected to another metal cylinder B of volume 1.0 m3 containing compressed
gas at 12 x 105 Pa as shown in Fig. 4. The taps X and Y are closed initially. Then tap X is
opened to allow the gas in the two cylinders mixed together. The temperature of the
cylinders A and B are kept at 25oC ( 298 K ).
( Given : Universal gas constant = 8.31 J K-1 mol-1
Avogadro constant = 6.02 x 1023 mol-1
tap X
A
)
tap Y
B
Fig. 4
a. If density of the gas in cylinder A and B is 1.55 kg m-3 at 25oC ( 298 K ). Estimate the
r.m.s. speed of the gas molecules. ( You can assume that the gas is an ideal gas )
( 2 marks )
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b. Calculate the final pressure in cylinder A and the number of moles of gas molecules that
has passed through tap X.
( 4 marks )
Tap Y is opened to inflate identical non-elastic balloons, each to a volume of 1.4 m3 at
atmospheric pressure of 105 Pa.
c. Find the work done against atmospheric pressure in inflating one balloon.
( 2 marks )
d. Calculate the number of balloons that can be inflated before the gas pressure in the
cylinder B drops below 5 x 105 Pa.
( 4 marks )
e. Briefly explain whether there is heat transfer between the cylinders and the surroundings
when the balloons are being inflated in the way described in this question.
( 2 marks )
5. a. Fig 5a shows an incompressible fluid flowing at a steady rate through a pipe with narrow
section in it.
Fig. 5a
i. Briefly explain why the fluid speeds up as it goes through the narrow section.
( 2 marks )
ii. What happens to the kinetic energy of the fluid moving towards the narrow section ?
How do you account for such a change in kinetic energy ?
( 2 marks )
b. A sail-board consists of a sail of area 1.5 m2. The mast can be tilted in any direction.
The dagger board is a vertical fin which can be pushed down into the water.
i. If the wind is blowing at a speed of 5.0 m s-1 in the direction of sailing, how the sail
should be oriented in order to achieve maximum speed. Estimate the maximum push
on the sail. State ONE assumption. Take the density of air to be 1.2 kg m-3.
( 4 marks )
ii. When sailing at 45o into the wind, show how the wind flows over the sail by copying
and then sketching streamlines on Fig 5b. Indicate the positions of high and low
pressure.
( 2 marks )
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Fig. 5b
Fig. 5c
iii. Fig.5c shows a force of 350 N acting on the sail which is set at 30o to the direction in
which the sail-board is traveling. Suppose the sail-board moves at a constant velocity.
Determine the drag and the sideway force acting on the sail-board.
( 2 marks )
Section B : Multiple Choices ( 23 marks )
1. A block of mass is falling from the top of a building. If the time taken for it to fall from
mid-height of the building to the ground is 0.40 s, find the total time taken for it to fall
from the top of the building to the ground. ( Neglect air resistance )
A. 0.68 s
B. 0.80 s
C. 1.20 s
D. 1.37 s
2.
An elastic cord has an unextended length of a. One end of the cord is attached to a mass
m and the other end is fixed. If the mass m performs an uniform circular motion on a
smooth surface, the period is T and the length of the elastic cord is 1.5 a. Now the
angular speed of the mass m is increased such that the length of the elastic cord is 2a.
Find the period of the motion. ( Assume that Hooke’s law is obeyed. )
2
T
3
B. 4T / 3
C. 2T / 3
A.
D.
3
T
2
3.
An object oscillates with SHM with O as the equilibrium position. The speed for it passes
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through points P and Q is the same. If the time taken for it to move from P to Q is 0.2 s
and then 0.3 s more to return to P again. Find the period of the motion.
A.
B.
C.
D.
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 correct ?
(1) When moving towards the lowest point of its path, the angular speed
(2)
(3)
A.
B.
C.
D.
5.
0.6 s
0.8 s
1.0 s
1.2 s
of the bob is increasing.
The centripetal acceleration of the bob is constant.
When the bob is at the lowest point, the tension in the string equals the centripetal
force.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
When mechanical resonance occurs in a slightly damped system, which of the following
statement(s) is/are correct ?
(1)
(2)
(3)
A.
B.
C.
D.
The amplitude of oscillation is at a maximum.
The natural and driving frequencies are equal.
The mechanical energy of the vibrating system is at maximum.
(1) and (2) only
(2) and (3) only
(1) and (3) only
(1), (2) and (3)
6. A flywheel of moment of inertia 4 kg m2, rotating at a rate of 10 rev s-1, is brought to rest
by an uniform frictional couple of 4N m after n revolutions. Find the value of n.
A. 50
B.
C.
D.
100
150
200
7. Two blocks A and B of mass 3 kg and 2 kg respectively are connected by a string passing
over a fixed smooth pulley. If A and B are released from rest, which of the following
statements is/are correct ?
(1)
The upward force acting on A by the string is equal to that on B.
(2)
The loss of P.E. in A is transferred to the gain of P.E. in B.
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(3)
The resultant force on A is equal to that in B.
A. ( 1) only
B. (2 ) only
C. (1) and (2) only
D. (1) and (3) only
8. A progressive wave in a stretched string has a velocity of 20 m s-1 and a frequency of 100
Hz. What is the phase difference between two points 2.5 cm apart along the string ?
A.
0
B.
/4
C.
/2
D.
/4
9. Which of the following statements about wave motion is/are correct ?
(1)
Diffraction cannot be exhibited by longitudinal waves.
(2)
Refraction is a result of change in speed of wave in different media.
(3)
A.
B.
C.
D.
10.
Reflection is sometimes accompanied by a phase change of  radians.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
Which of the following statements is/are correct ?
(1)
Radio waves can be polarized.
(2)
(3)
A.
B.
C.
D.
11.
Ultrasonic waves are electromagnetic in nature.
All standing waves are transverse.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
In a Young’s double slit experiment, a
monochromatic light source of wavelength 700 nm
is used and the separation of the slits is 0.1 mm. If
A.
B.
C.
D.
15 bright fringes are observed, what is the angle
subtended by those fringes at the center of the
double slit ?
4.8o
5.2o
5.6o
6.0o
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12.
Three Polaroid sheets, P, Q and R are placed along a straight line with a lamp and a
detector as shown.
Initially the directions of polarization P and Q are parallel, but are both normal to
that of R. What happens to the intensity I recorded by the detector when Q is being
rotated slowly through 90o until its direction of polarization is parallel to that of R ?
A. I increases throughout.
B. I decreases throughout.
C. I increases and then decreases.
D. I decreases and then increases.
13. An 1000 Hz sound is heard from a music store. A driver in a car is moving at a
constant speed of 30 m s-1. What are the apparent frequencies heard by the driver
when (a) the car is moving toward the music store and (b) the car is receding from
the music store ?
Take the speed of sound in air = 300 m s-1.
A.
(a)
900 Hz
(b)
1100 Hz
B.
C.
D.
910 Hz
1090 Hz
1100 Hz
1090 Hz
910 Hz
900 Hz
14. A convex lens P of focal length 20 cm and a
concave lens Q are placed 25 cm apart. Light
rays from an object O, which is 40 cm from P,
strikes normally on a screen at 35 cm away from
Q. Find the focal length of concave lens Q.
A. 10 cm
B. 15 cm
C. 20 cm
D. 25 cm
15. An air-wedge formed by two glass plates and a foil is illuminated normally by light
of wavelength . If a = 0.05 mm, L = 200 mm and the fringe separation d = 1.2 mm,
find value of .
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A.
B.
C.
D.
600 nm
550 nm
500 nm
450 nm
16. Suppose in a Newton’s ring experiment, the space
between the lens and the slab is filled with a liquid
of refractive index n. If the center of the
interference pattern in the reflected light is bright,
what conclusion can you draw about n ?
(1)
(2)
(3)
(4)
A.
B.
C.
D.
n1 < n < n2
n > n1; n > n2
n < n1; n < n2
n2 < n < n1
(2) only
(3) only
(2) and (3) only
(1) and (4) only
17. An astronomical telescope has an eye lens of focal length 20 mm. In normal
adjustment, when the final image of a distant object is at infinity, the separation of
the lenses is 500 mm. The angular magnification of the telescope under these
conditions is :
A. 22
B. 23
C. 24
D. 25
18. In an experiment, 32 tuning forks are arranged in the order of increasing pitch. The
fork of the highest pitch is exactly one octave ( double in frequency ) above that of
the lowest pitch. If any two adjacent forks are sounded together, the beat frequency
is always 8.0 Hz. What is the highest frequency among this set of forks ?
A. 256 Hz
B. 496 Hz
C. 512 Hz
D. 528 Hz.
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19. The graph shows the variation of the stress acting on a
wire with the strain produced. Which of the following
about the wire is/are true ?
(1) The value of Young modulus remains constant
until the wire breaks.
(2) It becomes more easy to stretch the wire after
P is reached.
(3) When the stress acted on the wire is 1.6 x 108
Pa, the wire will break.
A.
(1) only
B.
(3) only
C.
D.
(1) and (2) only
(2) and (3) only
20. Which of the following is NOT a basic assumption of the kinetic theory of an ideal
gas ?
A. All molecules move with the same speed at a certain temperature.
B. All molecules are point particles that have no physical size.
C. All collisions are perfectly elastic.
D. All molecules do not exert force on one another except during collisions.
21. An external work W is done on an ideal gas, while no heat is allowed to enter or
leave the gas. Which of the following statements is/are true ?
(1) The change produced is said to be isothermal.
(2) The change in internal energy of the gas is zero.
(3) There is an increase in the temperature of the gas if W is positive in value.
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only.
22. Two wires X and Y of the same length and of the same elastic metal are stretched to
the same tension. The diameter of wire X is double that of Y. The ratio of the elastic
potential energy stored in wire X to that stored in wire Y is
A. 1 : 2
B. 1 : 4
C. 2 : 1
D. 4 : 1
23. An uniform vertical steel wire is stretched by hanging a weight from its lower end.
Which of the following would put a greater strain on the wire ? ( The Young
modulus of steel is greater than that of brass )
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(1) Using a steel wire of greater unstretched length.
(2) Using a steel wire of greater cross-sectional area.
(3) Replacing the steel wire with a brass wire of the same unstretched length
and cross-sectional area.
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
Section C : Essay ( 24 marks )
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a. Use examples to illustrate the following situations :
i. an object may not necessary be at rest when the net force acting on it is zero.
ii. there may be no work done when force is applied to a moving object.
iii. a motion may be periodic but not isochronous.
( 6 marks )
b. Describe an experiment to demonstrate the relationship between the angular velocity of
a body performing circular motion with the radius of the path, for a constant applying
force. Explaining any source of errors.
( 6 marks )
2.
a. i. Describe an experiment, involving a double-slit arrangement, to demonstrate the
wave nature of light and to estimate its wavelength.
ii. Give further evidences that suggest that light wave is electromagnetic and
transverse ?
( 6 marks )
b. What is the principle of superposition ? Use this principle to explain (i) the formation
of beats and (ii) the formation of stationary waves.
( 6 marks )
3. a. i. Identify TWO differences between an ideal gas an a real gas.
ii. Sketch the distribution of molecular speed at a certain temperature for a fixed mass of
an ideal gas. Hence, explain the effect of temperature increase on the proportion of
molecules having speeds higher than a certain value.
iii. For an ideal gas under a certain temperature, find the relation between the
root-mean-square speed of the gas molecules and its molecular mass. Hence,
determine the ratio of root-mean-square speeds of hydrogen to oxygen, assuming
both behave ideally, at room temperature. ( Given : relative atomic mass of oxygen
is 16. )
( 6 marks )
b. Sketch graphs showing the variations of (i) the potential energy, and (ii) the force
between two molecules in solid matter as the separation between them is varied.
With reference to these graphs, explain the effects of
i. increasing the temperature of a solid to a high value, and
ii. increasing the mechanical loading force applied to a wire.
( 6 marks )
*** END OF PAPER ***
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Useful Formulae in Advanced Level Physics