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FINAL EXAMINATION
F.7 Physics Paper I
Time allowed – 3 hours
Answer ALL questions
1.
A block of mass M = 2 kg is placed on the surface of a light disc, as shown in Fig. 1.
The disc is depressed 100 mm vertically downwards and released.
100 mm
Fig. 1
(a)
Calculate the maximum permissible value of the force constant of the spring
so that the motion remains to be simple harmonic.
(2 marks)
Assume that the force constant of the spring is 200 Nm-1.
(b)
At 0.15 s after the block is released, what is its
(i)
position,
(ii)
velocity,
(iii)
acceleration?
(4 marks)
(c)
Suppose that the block is now at rest at its equilibrium position. A bullet of
mass m = 0.02 kg is fired vertically downwards at a high speed v = 300 ms-1
into the block and is embedded in it.
300 m s-1
Fig. 1(c)
(i)
(ii)
(iii)
2.
(a)
Find the velocity of the system just after the bullet is embedded in the
block.
Find the amplitude of the resulted simple harmonic motion.
What is the percentage of energy lost in this process?
(6 marks)
An object of mass 0.10 kg is suspended by a light string of length 5.0 m from a
fixed point. The object A is released from rest from a position such that the
taut string makes an angle of 60o with the vertical as shown in Fig. 2(a). Find
(i)
(ii)
the maximum speed of A during its subsequent motion, and
the maximum tension in the string.
(3 marks)
5m
60o
A 0.1 kg
Fig. 2(a)
(b)
The object A is now given a charge of 1.0 x 10-2 c, and a uniform electric field
of 1.0 x 102 V m-1 is introduced in a direction pointing vertically downwards
as shown in Fig. 2(b).
5m
o
60
A 0.1 kg
1.0 x 10-2 c
E
Fig. 2(b)
If the experiment in (a) is repeated, find
(i)
(ii)
the maximum speed of A, and
the maximum tension in the string.
(4 marks)
(c)
The object A still carries a charge of 1.0 x 10-2 c. However, this time a uniform
magnetic field of 10 T is introduced in a direction pointing out of the plane of
the paper as shown in Fig. 2(c).
˙
magnetic
induction 10 T
5m
60o
A 0.1 kg
1.0 x 10-2 c
Fig. 2(b)
3.
(a)
If the experiment in (a) is repeated,
(i)
What will then be the maximum seed of A?
(ii)
What will be the position of A and its direction of motion when the
tension in the string reaches its maximum value? Find this maximum
value.
(5 marks)
(i)
Explain the meaning of ‘plane polarized wave’. Give one example.
(ii)
State the conditions necessary for a stationary wave.
(4 marks)
(b)
(c)
A small source S emits electromagnetic waves of wavelength  (about a few
cm) which can be detected by an aerial A connected to a meter measuring the
intensity of the waves.
(i)
When the aerial A is at a distance d from S, the meter reading is I.
What is the meter reading if the distance SA is increased to 2 d?
(ii)
If the source is rotated through 90o about the line SA, the meter
reading falls to zero. Explain briefly.
(4 marks)
A metal reflecting screen is now placed some distance beyond A with its plane
perpendicular to the line SA as shown.
Refracting Screen
S
A
Fig. 3(c)
4.
(a)
(i)
Explain briefly why alternate maximum and minimum readings are
shown on the meter when the screen is moved slowly away from A.
(ii)
If the screen is displaced 9.0 cm between the first and the seventh
minimum, calculate the wavelength of the wave.
(4 marks)
Define the terms ‘tensile stress’ and ‘tensile strain’ regarding the stretching of
a wire.
(2 marks)
(b)
Within a wire, the atoms could be imagined to be arranged in a lattice with a
separation of x between each pair of atoms. The figure shows art of such a
crystal lattice with adjacent atoms linked by imaginary spring of force constant
k.
x
x
x
Fig. 4(b)
Derive an expression for the Young’s modulus E in terms of the force constant
k and separation x.
(4 marks)
(c)
(i)
The Young modulus for steel is 2.0 x 1011 Pa, and for aluminum, 7.2 x
1010 Pa. Compare their behavior under stress before the specimens
undergo plastic deformation?
(ii)
An aluminum wire and a steel wire, each of length 2.00 m, hang
vertically from a rigid beam and are spaced some distance apart. A
light horizontal beam, attached to their lower ends, carries a load of 50
kg at its mid-point. The diameter of the aluminum wire is 1.0 mm and
the loaded beam remains horizontal. Calculate
(1) the diameter of the steel wire
(2) the elastic potential energy of the system.
(6 marks)
5.
A cylinder fitted with a movable piston contains 1.00 mole of a monatomic gas at a
pressure of 1.00 x 105 Pa and a temperature of 200 K. The gas in first heated at
constant pressure to 350 K. Take the gas constant. R = 8.31 mol-1 K-1.
(a)
Find the volume of the gas
(i)
(ii)
before heating
after heating.
(2 marks)
(b)
Determine the change in internal energy of the gas.
(2 marks)
(c)
Determine the heat input to the cylinder.
(2 marks)
The gas is then compressed isothermally to its initial volume. Afterward, it is cooled at
constant volume to its initial temperature.
6.
(d)
Sketch the changes happened to the gas on a p-V diagram, inserting all the
initial and final pressure and volume values for all the processes described in
this question.
(3 marks)
(e)
What does the area bounded by the curves represent?
(f)
Mark on your curves in (d) the state of the gas when its density is highest.
(2 marks)
(1 marks)
Two glass sheets both of length 15 cm are separated by a thin foil with thickness 0.05
mm to form an air wedge. A monochromatic light with wavelength 560 mm is used to
observe the interference pattern.
 = 560 nm
0.05 mm
15 cm
Fig. 6
(a)
How do you know that the two glass sheets are perfectly flat?
(2 marks)
(b)
By use of a ray diagram, explain how a dark fringe is formed.
(2 marks)
(c)
Calculate
(i)
(ii)
the spacing between 2 adjacent bright fringes,
the total number of bright fringes that could be observed.
(2 marks)
(d)
What should be observed
(i)
(ii)
at the contact edge, and
at 2.1 cm from the contact point on the glass sheet?
(2 marks)
7.
(e)
If the contact side of the upper glass sheet is slowly lifted up until it becomes
horizontal, describe the change of the pattern that would be observed.
(2 marks)
(f)
Due to the gravitational force, the upper glass sheet bends slightly and curves
upwards after some time. What effect would this have on the pattern
observed?
(2 marks)
In the circuit shown in Fig. 7(a), a coil is connected in parallel with a neon lamp to a
I /A
cell of e.m.f. 2.0 V. The coil has a large inductance L. The neon lamp requires about
100 V to light it. When the switch is closed, the current I through the cell increases
with time as shown by the graph is Fig. 7(b).
S
neon lamp
2V
L
B
0.5
0.4
0.3
0.2
0.1
A
0
Fig. 7(a)
10
20
30
40
50
60
t/s
Fig. 7(b)
(a)
Explain the shape of the graph.
(2 marks)
(b)
From the graph, find the initial rate of change of the current with time. Hence,
calculate the inductance L of the coil.
(2 marks)
(c)
Describe and explain what happens when the switch is opened again one
minute after it is closed.
(2 marks)
S
2V
L
A
Fig. 7(c)
The neon lamp is now replaced by a 10 F capacitor and a diode as shown in
Fig. 7(c). Suppose the switch has been closed for a long time.
(d)
Describe and explain what happens to the capacitor when the switch is open,
stating the direction of any charge flow.
(2 marks)
(e)
Assume that no energy is dissipated in charging the capacitor. After the switch
is open for a long while, find the voltage across
(i)
(ii)
(iii)
8.
(a)
the capacitor,
the diode,
the coil.
(4 marks)
An inverting op amp is connected with an input resistor of 2.0 k and a
feedback resistor of 10 kA 1.5 V cell is connected across the input of the op
amp and a load of resistance 1.0 k is connected across the output.
Rf
I1
10 k
I
-
Rin
2 k
+
1 k load
1.5 V
Fig. 8(a)
(i)
(ii)
(iii)
Find the current, I1, drawn from the 1.5 V cell.
What is the voltage at the output of the op amp?
Find the current I.
(6 marks)
(b)
The circuit is re-connected to form a non-inverting op amp as shown.
Rf
I
10 k
1.5 V
+
Rin
2 k
1 k load
Fig. 8(b)
(i)
(ii)
(iii)
What is the voltage at the output of the op amp?
Find the current through the feedback resistor.
Find the power delivered to the load.
(6 marks)
9.
In a photoelectric experiment, monochromatic light source of power 5 W and
wavelength 120 nm is incident on the cathode. When the variable D.C. voltage is
gradually adjusted, the variation of the current I with V is obtained as shown below.
A
V
Fig. 9
(a)
Given: h = 6.63 x 10-34 Js and c = 3 x 108 ms-1, find
(i)
(ii)
(iii)
(iv)
(v)
the number of photons emitted per second,
the number of photoelectrons emitted,
Given: electronic charge e = 1.6 x 10-19C
the maximum kinetic energy of the photoelectrons,
the work function of the cathode,
the threshold frequency of the cathode.
(7 marks)
(b)
The tube in the above apparatus is made of quartz instead of glass. Explain
briefly.
(2 marks)
(c)
If a light source with the same intensity but double frequency is used, what
changes would occur? Sketch the I – V graph to show the difference.
(3 marks)
10.
The graph shows the activity, measured in counts per minute, of a radioactive sample
of 218
84 Po varied with time. It is known that -particles are emitted by the sample.
(a)
(b)
(i)
Write down the reaction equation representing the decay of Po-218,
use X to represent the daughter nuclide.
(ii)
238
It is known that 218
84 Po comes from
92 U after a series of radioactive
change. How many -particles and -particles have been emitted
during this radioactive series?
(3 marks)
(i)
Explain why the points on the graph do not fit exactly into the smooth
curve.
Estimate the half-life of Po-218 from the graph.
(2 marks)
(ii)
(c)
(i)
(ii)
(d)
The activity measured is the absolute decay rate.
(i)
(ii)
What is the decay constant of Po-218?
How long would it take for the activity to fall to 100 counts per
minute?
(3 marks)
Can this activity be measured by the GM tube? Explain briefly.
Estimate the initial mass of the sample of Po-218.
Given: Avogadro’s Number NA = 6 x 1023 mol-1
(4 marks)
END OF PAPER