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Final Mock Examination
Physics I
Time allowed : 3 hours.
1.
When told to open this question and answer book, check that all the questions are there. Look for the
words ‘END OF PAPER’ after the last question.
2.
ANSWER ALL QUESTIONS. Write your answer in the spaces provided in the question book. In
calculations you are advised to show all the main steps in your working.
3.
Assume: Velocity of light in air = 3 x 108 ms-1
Acceleration due to gravity = 10 ms-2
Question No.
Marks
1.
1
9
2
16
3
11
4
16
5
9
6
12
7
12
8
9
9
9
10
17
Total
120
An object of mass M = 0.4 kg rests on a smooth table. A bullet of mass m = 0.025 kg with
speed v0 = 450 m/s is fired horizontally towards the object. The bullet penetrates the object
and emerges from it. It is found that the object falls to the ground and lands at a point 30 m
from the table.
(a) (i) What is the time taken for the object to reach the ground? (2 marks)
(ii) Hence determine the horizontal component of the velocity of the object when it reaches the
ground. (2 marks)
(b) By using the principle of conservation of linear momentum, determine the velocity of the bullet
when it just emerges from the object. (2 marks)
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(c) Use the result of part (b) to compute the value of R, which is the distance of the bullet from the
table when it reaches the ground. (1 mark)
(d) What fraction of the kinetic energy is lost during the collision between the bullet and the object?
(2 marks)
2 (a) (i) The period of a pendulum is 2.2s. Its bob has a maximum speed of 0.46m/s and a mass
of 65 g. Calculate the maximum kinetic energy of the bob and the amplitude of the
oscillation (2 marks)
(ii) The figure (a) below shows how the kinetic energy W of the pendulum bob varies with time t.
Mark the axes with appropriate scales. (2 marks)
figure (a)
(iii) Sketch two more lines on the same graph, one to represent the variation of potential energy
with time and a second line to represent the total mechanical energy stored in the system.
Label these line “P.E” and “System energy” respectively. (2 marks)
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(b) A space shuttle crew is sent to service the Hubble Space Telescope H which is in a circular oibit
6.0105 m above the earth’s surface. The crew succeed in moving the space shuttle S into the
same orbit as H and its thrust rocket are shut down. The telescope is positioned a few
kilometres in front as shown in following figure. Let G be the gravitational constant and ME
the mass of the earth.
(Given : radius of the earth = 6.4  106 m)
(a)
What is the apparent weight of an astronaut of mass 75 kg inside the shuttle? (1 marks)
(b)
(i) Calculate the value of the gravitational field strength in the orbit.
(ii) Calculate the speed and period of the shuttle in the orbit.
(3 marks)
(4 marks)
(iii) Show that the total mechanical energy of the shuttle is proportional to 1/r, where r is
the radius of its orbit. (2 marks)
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3.
fo
v
O
S
R
Figure (a)
An audio source S is placed somewhere between an observer O and a reflecting plate R,
both lie on the same straight line perpendicular to the reflecting plate. Suppose the speed of
sound in air is c and a note of frequency fo is emitted from the source S.
(a)
The source is moving with speed v (v < c) towards the reflecting plate R.
(i) If f1 is the apparent frequency heard by the observer O for the wave comes
directly from the source S ,write down an expression for f1, in term of fo , c and
v.
(1 mark)
(ii) If f2 is the apparent frequency heard by the observer O for the wave reflected
from plate R, write the expression of f2, in term of fo , c and v. (1 mark)
(b)
Suppose S is moving at speed v = 2 ms-1, emitting a note of frequency 676 Hz. and
speed of sound is 340 ms-1.
(i)
How many beats per second will be observed for the two notes received by
the observer ?
(2 marks)
(ii)
The reflecting plate R then starts to move and at a particular speed vR The
beats is double to that in part(b)(i). (5 marks)
(I)
What is the apparent frequency received by the reflector?
(II)
Find vR.
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(III)
(c)
4.
In which direction is it moving ?
Mention two applications of Doppler effects
(2 marks)
The diagram shows a switched-range voltmeter
Voltage
selector
figure (a)
(i) The voltmeter is set to the 10V range. Find the output voltage from the op-amp when the input
is 10V. Your are not required to derive any formula you use. (2 marks)
(ii) The indicating meter has a resistance of 150. It needs a current of 2.0 mA for full scale
deflection. Calculate the value of R1 if the meter is to indicate full scale deflection when the
voltmeter input is 10V. (2 marks)
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(iii) Calculate the feedback resistances R2 and R3 for the 1V and 100mV ranges.
(3 marks)
(b)
1k
Figure (b)
(i)
Figure (c)
The circuit in Figure (b) shows an NPN silicon transistor and two resistors connected to a 6
V d.c. power supply. The current gain of the transistor is 100.
Calculate the value of the base current, stating clearly any assumptions you make. (2 marks)
Estimate the potential difference between the collector and the emitter ? Give reasoning for
your estimation. (3 mark)
(ii)
The same transistor is now used in the circuit in Figure c. Inputs 1 and 2 can be connected to
either +6 V d.c. or to 0 V. If an input is connected to +6 V it is said to be HIGH and if
connected to 0 V it is said to be LOW.
The output of the circuit is HIGH when the voltmeter reading is approximately 6 V and LOW
when the reading is close to 0V. Complete the following table for the circuit shown in Figure
(c) : (2 marks)
Input 1
LOW
LOW
HIGH
HIGH
Input 2
LOW
HIGH
LOW
HIGH
Output
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(iii) A student is now given two light-dependent resistors (LDRs) and a small d.c. buzzer. The
buzzer can be connected to the output of the circuit in Figure (c) and emits a loud noise when
the output is high but no noise when it is low.
The student is asked to add the two LDRs to the circuit in Figure (c) to produce an alarm
system. This system should emit a warning sound when the length of an object passing along
a conveyor belt is greater than the distance l between the two LDRs (see Figure (d) below).
Figure (d)
Each LDR is mounted in a cardboard tube and is illumined by a light beam falling directly
onto its surface. W
Complete the circuit diagram in Figure (e) below showing how the two LDRs should be
connected to perform the necessary task. (2 marks)
Figure (e)
Complete this circuit
by adding two LDRs
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5. (a) The diagram shows a beam of protons of mass m and charge q traveling at speed v and a
beam of alpha particles traveling at the same speed v. They both enter a region where a
uniform magnetic field B acts perpendicular to their direction of travel.
figure (a)
(i) Write down an expression for the force required to accelerate the protons in a circular path of rp.
(1 mark)
(ii)Write down an expression for the magnetic force acting on the protons. (1 mark)
(iii) Use the above expressions show that
q
v
(1 mark)

m Br p
(iv) Calculate the value r:rp where r is the radius of the path of the alpha particles.
(1 mark)
(v) Hence, on the figure (a) above, draw the path of the protons and the path of the alpha particles
after they enter the magnetic field. (2 marks)
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(b)
A student uses a flame probe to investigate the variations in potential in the region around a
positively charged sphere. The probe, in the form of a small gas flame at the point of a needle, is
connected to an electroscope calibrated to measure potentials.
(i)
The electroscope reading is a measure of the potential at the point where the probe is situated.
The experiment has to be performed with the charged sphere remote from the floor and
neighboring walls. Explain briefly why. (1 mark)
(ii)
Figure (c)
The student measures the potential at points A and B (see Figure (c)), which are 1 cm apart.
He finds that the potentials at A and B are 450 V and 400 V respectively. Give an estimate of
the electric field in the region between A and B. In what direction does it act ? (2 marks)
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6 (a)
Figure (a)
Figure a shows an aluminum plate with a current of 50 mA passing through it.
(i)
Calculate the average drift velocity of the conducting electrons, given that there are
1029 conducting electrons per m3 of aluminum and the charge of an electron is 1.6 
10-19 C. (2 marks)
(ii)
A uniform magnetic field of 1.5 T is now applied normally downwards to the plate and
covers whole surface area. Mark on Figure (a) the direction of the force experienced by
each electron and calculate its magnitude. (3 marks)
(b) An experiment is being set up to demonstrate the Hall voltage and it is decided to use a
germanium slice. The circuit diagram for the experiment is shown in Figure (b) below
(i)
(ii)
Figure (b)
Explain why a germanium slice was chosen in this experiment instead of an aluminum
plate. (2 marks)
After switch S has been closed, a small p.d. is found to exist between X and Y even in
the absence of a magnetic field. Explain why this is so. How would you arrange X and
Y to be at the same potential ? (2 marks)
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(d)
A uniform magnetic field of 0.2 T is now applied acting perpendicularly downwards into the
plane of the paper, covering the whole surface of the slice. If the reading of the milliammeter
is 1 mA, estimate the Hall voltage that exists across the slice.
(the thickness of the slice = 0.1 mm,
number of charge-carriers per unit volume for germanium = 1020 m-3,
the charge on each carrier = 1.610-19 C.)
(e)
(2 marks)
Mention one practical application of the Hall effect. (1 mark)
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7. (a) State Faraday’s law of electromagnetic induction. ( 1 mark)
(b) An exhibit at a science museum consists of three apparently identical vertical tubes, T1, T2 and
T3, each about 2 m long. With the tubes are three apparently identical small cylinders, one to
each tube.
figure a
When the cylinders are dropped down the tubes those in T1, T2 and T3 , arrange the time required
for the cylinders to reach the bottom in ascending order. Explain briefly. (4 marks)
(c)
figure (b)
figure (c)
A d.c. source of 200 V supplies power to a circuit containing a motor with armature resistance 5 ,
a switch S, a rheostat R and an ammeter A, all connected in series. After the switch S is closed, the
reading on the ammeter changes with time as shown by the curve in Figure (c).
(a) Calculate the resistance of the rheostat R. (2 marks)
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(b)
After the motor has reached constant speed, calculate
(i)
the back e.m.f. of the motor, (2 marks)
(ii)
the mechanical power output of the motor, and (2 marks)
(iii) the power dissipated as heat in the armature. (1 mark)
8 (a)
direction of ball
(i)
Figure (a)
Figure (a) shows the streamlines around a tennis ball when it is projected in a straight
line through still air. If, apart from the forward motion, it is also spinning about an axis,
through its centre, perpendicular to the plane of paper in an anti-clockwise direction
according to figure (b).
forward motion
Figure (b)
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Describe, with reasons, the subsequent motion of the ball. (4 marks)
(b)
(i)
One end of an open tube is put vertically into water. By blowing strongly across the
open end, water can be drawn up the tube. Suppose a few centimetres of the tube is
above the water surface. What should be the air velocity at the open end for water in
the tube to rise up by 1 cm? Explain your working. (Surface tension effects may be
ignored.)
( Density of air
Density of water
Acceleration due to gravity
(ii)
=
=
=
1.29 kg m-3,
1 000 kg m-3,
10 m s-2 )
(3 marks)
Mention two daily applications making use of the principle described in (b)(i).
(2 mark)
9. A circular wire ring is dipped into soap solution and held vertically. When viewed in a dark
room with monochromatic light of wavelength 6.5  10-7 m reflected normally from the film, a
series of interference fringes are seen. The pattern of fringes at a particular instant is shown is
Figure (a) (The refractive index of soap solution = 1.33)
Figure (a)
(a)
What colour are the fringes ? ( 1 mark)
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(b)
Why is there dark area at the top of the ring ? (2 marks)
(c)
What is the thickness of the film at point A ? (3 marks)
(d)
As time goes on and if the film drains downwards and does not break, the fringe pattern
changes from that shown in Figure (a) describe the changes you would expect to see
(explanation are not required). (3 marks)
10. (a) It is thought that an extremely short-lived radioactive isotope
-emission, has a half-life of 200s.
269
110
X , which decays by
After a series of  decays the element
A
104
Y is
formed from the original isotope. There are no  decays.
(i) Deduce the value of A (2 marks)
(ii) Calculate the decay constant  of
(iii) The number of nuclei of
activity of 0.54 g of
269
110
269
110
269
110
X (2 marks)
X in a sample of mass 0.54 g is 1.2 x 1015.
Determine the
X . (2 marks)
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(iv) Why is the above calculated value for the activity is only an approximate? (1 mark)
(b)
In a fusion reaction, two nuclei of the isotope of hydrogen 12 H (called deuterium) fuse
together producing another isotope of helium 23 He and a neutron.
(
Mass of the deuterium nucleus = 2.015 u
Mass of the helium nucleus =3.017 u
Mass of neutron = 1.009 u
Atomic mass unit 1u = 1.66x10-27 kg. )
(i) Write an equation for the above fusion reaction. (1 mark)
(ii) Explain how and why the mass of a helium
3
2
He atom differs from the sum of the masses of
its constituent particles. (2 marks)
(iii) Calculate the energy released by fusion of 1 kg of deuterium. (3 marks)
(iv) If 50% of the energy released in part (c) were used to produce 1 MW of electricity
continuously in a station, for how many days would the station be able to function?
(2 mark)
(v) The energy released in each fusion reaction is smaller than that in each fission reaction. State
two reasons why it would still be advantageous if an operational fusion reactor could be
developed.
(2 mark)
End of paper
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