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THE INCREDIBLE COLLEGE
A-LEVEL MOCK EXAMINATION
Marker’s
Use Only
PHYSICS PAPER I
Question/Answer Book
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Time allowed : 3 hours
This paper must be answered in English.
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INSTRUCTIONS
6
1.
This section carries 120 marks.
2.
Answer ALL questions.
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Total
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Useful Formulae in Advanced Level Physics
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i. Answer ALL questions.
ii. Write your answers in the spaces provided in this question/answer book. In calculations
you should show all the main steps in your working.
iii. Assume : velocity of light in air = 3  108 m s1
acceleration due to gravity = 10 m s2
1. A pendulum bob of mass 200 g is set to whirl in a horizontal circle by a light inextensible
string. A hollow glass rob supports the string as shown in Figure 1. The air resistance and
the friction between the string and the glass rod are negligible.
Figure 1
(a) The bob is moving at a rate of 40 revolution per minute with a radius of 30 cm.
(i) Find the angular velocity of the bob and the centripetal force required.
(2 marks)
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1. (a) (Continued)
(ii) Sketch a diagram to show all the forces acting on the bob.
(2 marks)
(iii) Hence determine the tension of the string.
(2 marks)
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(b) Now the radius of the circle described by the bob is reduced from 30 cm to 20 cm.
(i) Find the new moment of inertia of the bob about the glass rod.
(1 mark)
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(ii) Hence determine its new angular velocity.
(2 marks)
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1. (b) (Continued)
(iii) Calculate the change in kinetic energy of the bob. Explain briefly. (2 marks)
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(iv) State the change in the angle of depression of the bob with the horizontal.
(1 mark)
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2. An experimental car is fitted on its suspension system with 4 identical springs without
shock absorbers. The car is lowered onto the ground and the springs are 10 cm shorter than
their unstressed length. The effective mass of the car is 1200 kg. Assume the mass of the
car is evenly distributed and the springs obey Hooke’s law.
(a) What is the force constant of the spring?
(2 marks)
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(b) In a test, the car is forced downwards by a further 8 cm, released and allowed to
oscillate.
(i) Show that the oscillation of the car is simple harmonic.
(2 marks)
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2. (b) (i)
(Continued)
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(ii) What is its period of oscillation?
(2 marks)
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(c) If the car is loaded with an evenly distributed mass of 300 kg before test, find
(i) the new period of oscillation and
(1 mark)
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(ii) the maximum amplitude of oscillation which will allow the load to remain in
contact with the car throughout the motion.
(2 marks)
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(d) Shock absorbers are now fitted to the car to damp oscillations. Sketch on the same
graph, the displacement-time curves of the car for at least 2 cycles when it undergoes
oscillation with and without shock absorbers.
(3 marks)
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2. (d) (Continued)
Displacement
Time
3. (a) A stretched string of length 0.3 m produces stationary wave of fundamental frequency f0.
Velocity of sound in air is 330 ms1.
(i) Sketch the waveform of the wave along the string at fundamental frequency.
(1 mark)
(ii) Hence find the fundamental frequency f0.
(1 mark)
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(iii) If the mass per unit length of the string is 3  103 kgm1, find the tension in the
string.
(Given : velocity of propagation of wave along a string =
Tension in the string
)
(2 marks)
Mass per unit length of the string
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3. (a) (Continued)
(iv) Explain why sounds of the same note produced by two different instruments can be
readily distinguished.
(1 mark)
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(b) A certain machine in a construction site produces a 95 dB intensity level when
operating.
(i) Find the maximum number of machines that can be operating at the same time in
the site if the noise level is not allowed to exceed 100 dB.
(3 marks)
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(ii) Suppose the background produces a noise level of 90 dB. Would the total noise
level exceed the noise limit of 100 dB when the number of machines operating in
the construction site found in (b)(i) is maximum?
(4 marks)
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4. (a) Two whistles of the same frequency, separated by 2 m, are blown simultaneously. An
observer moves along a line 50 m away from and parallel to the line joining the whistles.
Minima of sound are heard at successive points that are 0.85 m apart. Calculate the
frequency of the whistles. (Given : speed of sound in air = 340 ms 1 )
(2 marks)
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4. (Continued)
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(b) Explain why it is unable to observe light interference as in part (a) using two similar and
separate light sources, even if the dimensions of the apparatus are suitably modified.
(2 marks)
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(c) A laser beam of wavelength 600 nm passes through a double-slit and forms an
interference pattern on a screen placed 2 m away. A student finds that the distance
between the centres of the 1st bright fringe and the 8th bright fringe is 84 mm.
(i) What is the slit separation?
(2 marks)
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(ii) Explain both qualitatively and quantitatively what will happen to the fringes if a
thin transparent sheet of thickness 15 m is placed in front of one of the slits.
(Given : refractive index of the sheet = 1.4)
(3 marks)
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(iii) What is the change in the interference pattern if the whole set-up is immersed in
water? Explain briefly.
(1 mark)
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4. (c) (Continued)
(iv) Now the double-slit is replaced by a fine diffraction grating of 600 lines per mm.
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Determine how many bright lines can be observed on the screen.
(2 marks)
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5. (a) Two solid spherical conductors of radii 30 cm and 10 cm respectively are placed a
considerable distance apart in vacuum such that the presence of each sphere does not
affect the charge distribution on the other. Each sphere carries a charge of 3.0  10 8 C .
1
= 9.0  10 9 N m 2 C  2 )
(Given :
40
(i) Find the electric field strength and the electric potential at the surface of each
sphere.
(2 marks)
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(ii) Now the two spheres are joined by a thin conducting wire. A re-distribution of
charge between the two spheres occurs. Determine the value of charge on each
sphere.
(4 marks)
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5. (Continued)
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(b)
Figure 5.1
(i)
Figure 5.2
Figure 5.1 shows a potentiometer circuit. The potentiometer wire AB is of length
1 m. The e.m.f. of the battery M is 9 V. A balance point is obtained at 27 cm from
A when a standard cell of e.m.f. 1.8 V is connected across PQ.
(1) What is the maximum e.m.f. that can be measured by the potentiometer?
(1 mark)
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(2) What is the function of the rheostat R in the circuit in Figure 5.1 ?
(1 mark)
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(ii) Now, the standard cell is disconnected and a cell E, which is in parallel with a
20  resistor and a switch K shown in Figure 5.2, is connected across PQ. A
balance point is obtained at 30 cm from A when K is opened , and 25 cm from A
when K is closed. Calculate the e.m.f. of the cell E and its internal resistance.
(4 marks)
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6. (a) State the laws of electromagnetic induction.
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(2 marks)
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(b) MN and PQ are two smooth horizontal rails which are 0.5 m apart and of negligible
electrical resistance. Two resistors, each of resistance 2 , are connected across MP
and NQ to form a rectangular loop. A uniform magnetic field of intensity B = 2.0 T,
pointing into the paper, is set up in the region MNQP. A smooth metal rod XY of
resistance 1  is pulled along the rails by a constant horizontal force F  0.2 N as
shown in Figure 6. The rod attains a terminal speed v eventually.
X
M
2
N
B
F
2
P
Q
Y
Figure 6
(i)
Account for the motion of the rod XY.
(2 marks)
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6. (b) (Continued)
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(ii) Determine the direction of the induced current in the rod XY.
(1 mark)
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(iii) When it has reached its terminal speed v, determine
(1) the induced current I in the rod XY,
(1 mark)
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(2) the induced e.m.f.  in the circuit, and
(2 marks)
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(3) the terminal speed v.
(1 mark)
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(iv) Calculate the mechanical power developed by the applied force and the total power
loss through the resistors at the instant. Comment on the results.
(3 marks)
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7. A circuit with a NPN transistor is shown in Figure 7.1. The currents pass through resistor
R1, R2 and RL are I1, I2 and IL respectively. It is given that R1 = 500 k, R2 = 85 k,
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RL = 3.5 k, Vin = 6 V, VBE = 0.7 V and VCC = 6 V.
VBE
Figure 7.1
(a) Determine
(i) the value of I2 by considering the p.d. across R2,
(1 mark)
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(ii) the value of I1,
(2 marks)
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(iii) the value of base current IB,
(2 marks)
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(b) If the current gain  is 100, determine
(i)
the value of IL,
(1 mark)
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(ii) the value of Vout,
(1 mark)
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7. (Continued)
(c) Is there any problem in the above configuration when the input voltage is varied?
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(1 mark)
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(d) What is the suitable value of RL so that the circuit can be operated with output at
maximum symmetrical swing and not easily to be saturated?
(2 marks)
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(e) After the resistor mentioned in part (d) has been installed, an input voltage Vin is applied
to the circuit. If the input voltage has the form as shown in Figure 7.2, sketch the output
voltage versus time in the space provided below.
(2 marks)
Figure 7.2
Vout
t
8. (a) A frame of negligible mass is attached to a copper wire of length 1 m and
cross-sectional area 0.3 mm2. The Young modulus of copper is 1.1 1011 Nm2. A
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block of mass 5 kg is raised to a height h = 80 cm and dropped onto the frame, it
rebounds to a height of 20 cm, producing a temporary extension and stress in the wire.
Figure 8.1
(i)
Find the velocities of the block just before and after impact.
(2 marks)
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(ii) If the block is in contact with the frame for 0.2 second, find the total resultant force
on the frame during the impact.
(1 mark)
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(iii) Determine the stress produced.
(1 mark)
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8. (a) (Continued)
(iv) Determine the extension produced.
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(1 mark)
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(v) If the copper wire is replaced by a metal wire of double cross-sectional area and
double Young modulus, what will be the extension compared with that in (b)(iv) if
the same block is dropped onto the frame from the same height?
(1 mark)
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(b) Consider two identical atoms, initial separation, being brought closer together. The
potential energy (of either atom) is given by
A
B
U= 
+
6
12
r
r
where r is the separation between the two atoms.
(i)
dx n
 nx n 1 )
dx
(1 mark)
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Find the expression of the force F in terms of A and B. (Hint :
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(ii) Determine the equilibrium separation of the atoms.
(Given : A  1.565  10 79 J m 6 and B  4.372  10 137 J m12 )
(1 mark)
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k
where r0 is the equilibrium separation
r0
and k is the force constant between two atoms. If k is equal to the minus slope of
F-r graph at equilibrium separation, find the Young modulus of the solid.
(2 marks)
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(iii) Young modulus can be expressed as E =
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8. (b) (iii) (Continued)
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(iv) When atoms are gradually moved apart, at what separation will the atomic
interaction be broken down?
(2 marks)
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9. In the X-ray tube as shown in Figure 9.1, the accelerating voltage is 100 kV. X-rays are
produced when the tungsten target is bombarded by fast moving electrons. The X-ray
spectrum is shown in Figure 9.2.
(Given : h = 6.63  1034 Js, e = 1.6  1019 C and c = 3.0  108 ms1)
Figure 9.1
Figure 9.2
(a) Calculate the kinetic energy, in J, of the electrons before they hit the target?
(2 marks)
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9. (a) (Continued)
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(b) Suppose there are 3.751016 electrons striking the target per second. What must be the
power P supply to X-ray tube?
(2 marks)
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(c) A student says that this power is transferred to the electrons from the heat of the cathode.
Do you agree with the student? Explain briefly.
(2 marks)
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(d) Suppose the kinetic energy of an electron is completely transferred to a target atom, find
the minimum wavelength 0 of the X-ray photon.
(2 marks)
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(e) Sketch on Figure 9.2 to show how X-ray spectrum is changed by reducing the
accelerating voltage to one-half.
(2 marks)
(f) Suggest TWO criteria for the choice of the target material. Give reasons to support your
answer.
(2 marks)
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10. (a) In a Rutherford scattering experiment the gold target ( 197
79 Au ) is bombarded by
-particles. One of the -particles happens to collide head-on with a target nucleus
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which remains at rest all the time.
(i) Find the minimum distance of approach of the -particle if its kinetic energy is
1
6.5  10 13 J . (Given :
= 9.0  10 9 N m 2 C  2 and e  1.6  10 19 C )
40
(2 marks)
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(ii) Write down an approximate value for the ratio of atomic radius of gold to its
nuclear radius. Hence estimate the density of the nucleus of a gold atom.
(Given : atomic radius of gold is 1.44  10 10 m and density of gold is
(3 marks)
19.3  103 kg m 3 )
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(b) 1 cm3 of liquid containing 24 Na atoms is injected into the blood stream of a dog. The
initial activity of the 24 Na sample is 3000 Bq. Five hours later, 1 cm3 of blood is taken
out of the dog's body and at that instant the activity of this sample is found to be 10 Bq.
(Given : half-life of 24 Na = 15 hours)
(i)
Calculate the initial number of 24 Na atoms.
(2 marks)
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10. (b) (Continued)
(ii) Find the volume of the blood inside the dog. State your assumptions. (4 marks)
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(c) State TWO uses of radioisotopes.
(1 mark)
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END OF PAPER
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