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Class Index Number Name
14
ST. ANDREW’S JUNIOR COLLEGE
JC 2 2015
Preliminary Examination
Paper 2
PHYSICS, Higher 2 9646
2nd September 2015 1 hour 45 minutes
(08:00 – 09:45)
Candidates answer on the question paper.
No additional materials are required.
READ THESE INSTRUCTIONS FIRST
Write your name, index number and Civics Group on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams, graphs or rough working.
Do not use paper clips, highlighters, glue or correction fluid.
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part
question.
For Examiner’s Use
1 / 6
2 / 10
3 / 9
4 / 10
5 / 10
6 / 15
7 / 12
Total / 72
This question paper consists of 24 printed pages including this page.
SAJC 2015 Preliminary Examination / 9646 [Turn Over
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Data
speed of light in free space, c = 3.00 x 108 m s-1
permeability of free space, o = 4 x 10-7 H m-1
permittivity of free space, o = 8.85 x 10-12 F m-1
= (1/(36)) x 10-9 F m-1
elementary charge, e = 1.60 x 10-19 C
the Planck constant, h = 6.63 x 10-34 J s
unified atomic mass constant, u = 1.66 x 10-27 kg
rest mass of electron, me = 9.11 x 10-31 kg
rest mass of proton, mp = 1.67 x 10-27 kg
molar gas constant, R = 8.31 J K-1 mol-1
the Avogadro constant, NA = 6.02 x 1023 mol-1
the Boltzmann constant, k = 1.38 x 10-23 J K-1
gravitational constant, G = 6.67 x 10-11 N m2 kg-2
acceleration of free fall, g = 9.81 m s-2
Formulae
uniformly accelerated motion, s = u t + ½ a t2
v2 = u2 + 2 a s
work done on/by a gas, W = p V
hydrostatic pressure, p = g h
gravitational potential, = Gm
r
displacement of particle in s.h.m., x = xo sin t
velocity of particle in s.h.m., v = v0 cos t
v = x 02 x 2
mean kinetic energy of a
molecule of an ideal gas, E = 3 kT
2
resistors in series, R = R1 + R2 + ...
resistors in parallel, 1/R = 1 / R1 + 1 / R2 + ...
Q
electric potential, V =
4 0r
alternating current/voltage, x = xo sin t
transmission coefficient, T α exp(-2 k d)
8 π 2 m (U E)
where k =
h2
radioactive decay, x = xo exp (- t)
0.693
decay constant, =
t1 / 2
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1 (a) An electric water heater contains a tube through which water flows at a
constant rate. The water in the tube passes over a heating coil, as
shown in Fig. 1.1.
Fig. 1.1
The water flows into the tube at a temperature of 18 ºC. When the
power of the heater is 3.8 kW, the temperature of the water at the outlet
is 42 ºC. The specific heat capacity of water is 4.2 J K-1 g-1.
(i) Use the data to calculate the flow rate, in g s-1, of water through
the tube.
flow-rate = …………………………… g s-1 [2]
(ii) State and explain whether your answer in (i) is likely to be an
overestimate or an underestimate of the flow rate.
………………………………………………………………………….
..…………………………………………………………………………
……………………………………………………………………….[2]
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(b) A student throws a basketball into the air and then suggests that the
change in potential energy of the gas in the basketball as it rises will
cause a similar change to its internal energy. State and explain if the
student is right.
…..………………………………………………………………………………
..…………………………………………………………………………………
……………………………………………………………………………….[2]
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2 (a) A student sets up the experiment shown in Fig. 2.1 to demonstrate two-
source interference. The student could not observe any interference
pattern formed on the screen.
2 narrow
slits
Light Bulb
screen Fig. 2.1
(i) State why there is no interference pattern formed in the set up
above.
…………………………………………………………………………
………………………………………………………………………..[1]
(ii) State a modification to the setup so that an interference pattern
can be observed.
…………………………………………………………………………
………………………………………………………………………..[1]
(b) In order to determine the speed of sound in air, an experiment shown
in Fig. 2.2 is carried out. A source of sound is placed several metres
from a plane reflecting wall. A microphone, connected to a cathode-ray
oscilloscope (c.r.o.) is used to detect nodes and antinodes along the
line XY between the source and the wall. The microphone is moved
from one antinode through 20 nodes to another antinode, a distance of
1.20 m.
wall
antinode antinode
1.20 m
microphone
Source of X Y
sound c.r.o.
Fig. 2.2
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Fig. 2.3 shows the display on the c.r.o. at X and Y. The time-base control
is set to 0.1 ms / cm.
1 cm
Fig. 2.3
1 cm
(i) Explain what is meant by a node and why there are nodes
between the source and the wall.
………………………………………………..…………………………
…………………………………………..………………………………
…………………………………………..………………………………
…………………………………………..………………………………
…………………………………………..………………………………
…………………………………………..……………………………[3]
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(ii) Calculate the frequency of the sound wave.
frequency = …………………………… Hz [2]
(iii) Calculate the speed of sound.
speed = …………………………… m s1 [3]
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3 (a) A bubble chamber is an apparatus filled with superheated transparent
liquid that is used to show the paths of particles.
A high-energy particle enters a chamber and, at a point P, there is a
reaction that gives rise to two particles. The tracks of the particles are
shown in Fig. 3.1.
Fig. 3.1
There is a uniform magnetic field acting normally to the plane of the
paper.
(i) The path of each of the two particles produced in the reaction is
a spiral. State why they spiral in opposite directions.
……………….…………………………………………………………
………………………………………………………………………[1]
(ii) Suggest why each path is a spiral, rather than a circle.
…………………………………………………………………………
…………………………………………………………………………
…………………………………………………………………………
……………………………………………………………………….[2]
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(b) A large horseshoe magnet produces a uniform magnetic field of flux
density B between its poles. Outside the region of the poles, the flux
density is zero. The magnet is placed on a top-pan balance and a stiff
wire XY is situated between its poles, as shown in Fig. 3.2.
Fig. 3.2
The wire XY is horizontal and normal to the magnetic field. The length
of wire between the poles is 4.4 cm. A direct current of magnitude
2.6 A is passed through the wire in the direction from X to Y. The
reading on the top-pan balance increases by 2.3 g
(i) State and explain the polarity of the pole P of the magnet.
…………………………………………………………………………
………………….……………………...………………………………
……………………………………….…………...……………………
………………..…………………………………………………….[2]
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(ii) Calculate the flux density between the poles.
flux density = ……………… T [2]
(iii) The wire has a cross-sectional area of 1.26 x 10-5 m2 and the
number of conduction electrons per unit volume is
8.46 x 1028 m-3.
Calculate the average speed of the conduction electrons.
speed = …………………m s-1 [2]
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4 (a) A small rectangular coil ABCD contains 140 turns of wire. The sides AB
and BC of the coil are of lengths 4.5 cm and 2.8 cm respectively, as
shown in Fig. 4.1.
Fig. 4.1
The coil is held between the poles of a large magnet so that the coil
can rotate about an axis through its centre. The magnet produces a
uniform magnetic field of flux density B between its poles.
When the current in the coil is 170 mA, the maximum torque produced
in the coil is 2.1 x 10-3 N m.
(i) Calculate the magnetic flux density B between the poles of the
magnet. Show your working.
flux density = …………………….. T [4]
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(ii) The current in the coil is switched off and the coil is positioned as
shown in Fig. 4.1.
The coil is then turned through an angle of 900 in a time of 0.14 s.
Calculate the average e.m.f. induced in the coil.
e.m.f. = ……………… V [2]
(b) An ideal iron-cored transformer is illustrated in Fig. 4.2.
Fig. 4.2
Fig. 4.3 shows the variation with time of the current IP in the primary coil.
There is no current in the secondary coil.
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Fig. 4.3
Fig. 4.4
Fig. 4.5
(i) Complete Fig. 4.4 to show the variation with time t of the
magnetic flux in the core. [1]
(ii) Complete Fig. 4.5 to show the variation with time t of the e.m.f. E
induced in the secondary coil. [2]
(iii) Hence state the phase difference between the current IP in the
primary coil and the e.m.f. E induced in the secondary coil.
phase difference = ……………rad [1]
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5 (a) Three alpha particles with equal energies are fired towards the nucleus
of a gold atom.
Complete the diagram, showing the possible paths of the alpha
particles (labeled A, B and C) as they pass by, and then move away
from the nucleus. [2]
B
C
gold nucleus
(b) In 1991, an English archaeologist discovered the well-preserved
remains of the Iceman trapped in a glacier in the Italian Alps.
Radioactive dating was used to obtain his age. A 50.0 g sample of
carbon was taken from the pelvic bone of the remains of the Iceman
and was found to have a 14C decay rate of 200.0 disintegrations per
minute. It is known that carbon from 1.0 g of a living organism has a
decay rate of 15.0 disintegrations per minute. The half–life of the 14C
isotope is 5700 years.
(i) Determine the decay constant of the 14C isotope.
decay constant: ……………….. s-1 [1]
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(ii) Hence determine the age of the Iceman.
age of iceman = ………………… years [3]
(iii) Suggest why 11C isotope with a half-life of 1224 s is not used in
radioactive dating.
.......................................................................................................
...................................................................................................[1]
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(c) Three bottles of water and some rocks can provide, in theory, enough
energy for the consumption of a family for one year. The water and
rocks can be used to obtain the raw materials for a thermonuclear
reaction that can take place between deuterium (hydrogen-2) and
tritium (hydrogen-3).
Deuterium can be extracted from water whereas tritium can be made
from lithium, which can be extracted from the rocks. After extraction,
thermonuclear reactors heat a mixture of deuterium and tritium to 100
million degrees Celsius to produce the reaction shown below.
2
1 H 31 H 42 He 01 n
(i) Given the masses of the following particles, calculate the
amount of energy produced in this reaction.
deuterium: 3.3445 1027 kg,
tritium: 5.0083 1027 kg,
α-particle: 6.6465 1027 kg and
neutron: 1.6750 1027 kg.
energy = ………………… J [2]
(ii) Explain why it is necessary that the temperature be so high for
this reaction to occur.
…………………………………………………………………………
………………………………………………………………………[1]
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6 The variation with temperature of the resistance of a thermistor is shown in
Fig. 6.1.
60000
50000
40000
resistance R / 30000
20000
10000
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
temperature / oC
Fig. 6.1
(a) Some data from Fig. 6.1 are used to plot the graph of Fig. 6.2.
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11.0
10.5
10.0
9.5
9.0
ln (R / ) 8.5
8.0
7.5
7.0
6.5
6.0
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
1
/ 103 K 1
Fig. 6.2 T
The relation between resistance R and T is thought to follow the
expression
B
R Ae T where T is in kelvin.
(i) Use Fig. 6.1 to determine ln (R / ) for a temperature of
25 oC.
ln (R / ) = …….……………………[2]
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(ii) On Fig. 6.2,
1. plot the point corresponding to temperature of 25 oC, [1]
2. draw the line of best fit for the points. [1]
(iii) Use the line drawn in (ii) to determine the constants A and B in
the expression in (a).
A = …..………..……..………
B = ………...…..………… [3]
(b) (i) This thermistor is more sensitive when used as a thermometer
in low temperature measurements. Suggest a reason for this
based on Fig. 6.1.
……..…………………...………………..……………………………
……………………….…………………………………………..……
……….……………………………………………………………..[1]
(ii) A thermistor is made up of semiconductor material. Explain
why its resistance decreases as temperature increases.
……..…………………...………………..……………………………
……………………….…………………………………………..……
……….……………………………………………………………..[1]
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(iii) Fig. 6.3 shows the variation with temperature of the resistance
of some common materials in comparison with a thermistor.
at 20 oC at 100 oC
A copper wire 1.0 1.3
A wire of constantan 31.0 31.1
Bead thermistor 5000.0 80.0
Fig. 6.3
1. Describe the main difference in the variation with temperature of
the resistance between the bead thermistor and the two other
metals.
……..…………………...………………..……………..…………………
…………………….……………………………………………………….
………………………………………………………………………….[1]
2. A device is used in motors to limit a possible surge of current when
the motor is switched on at a temperature of 20 oC. Suggest why it
is preferable for the device to be a bead thermistor rather than a
constantan wire.
……..………………….....………………..………………………………
…………………….……………………………………………………….
…………………………………………………..…………………………
……………………………………………….…..……………………..[2]
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(c) A circuit suitable for temperature measurement is a Wheatstone bridge
with a thermistor used as one bridge leg as shown in Fig. 6.4. Any
change in temperature will cause a change in the value of the
thermistor RT so that there is a significant potential difference between
X and Y which is connected to a data logger.
R R
E
X Y
R RT
Fig. 6.4
R - RT
The potential difference between Y and X is given as VYX E.
2( R RT )
A thermistor with the characteristics shown in Fig. 6.1 is used. The
temperature of the system to be measured has a range from 5 oC to
40 oC. If the value of R used is 40 k and E is 10 V, determine the
minimum and maximum value of VYX.
minimum = ….……….....……………V
maximum = ……..……….….............V [3]
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7 When a sound is produced in a large hall, multiple reflections occur at the
walls (Fig. 7.1). It can take an appreciable time for the reflections to die away.
This effect is known as reverberation, and sometimes leads to poor quality
acoustics if care is not taken in the design of the hall.
Fig. 7 .1
One way of reducing reverberation is to use sound-absorbing materials for the
seating and walls of the hall. It is known that the absorption of sound is
frequency-dependent.
Design an experiment to investigate how the amplitude of the reflected sound
from a particular surface depends upon the frequency of the incident sound.
The equipment available includes the following:
tuning forks of various frequencies microwave transmitter
microphone signal generator
loudspeaker amplifier
dual-beam CRO
You should draw a labelled diagram showing the arrangement of apparatus
you would use. In your account, you should pay particular attention to
(a) the identification and control of variables,
(b) the equipment you would use,
(c) the procedure to be followed,
(d) the method of measuring the frequency of the incident sound,
(e) the method of measuring the amplitude of the reflected waves,
(f) any precautions that would be taken to improve the accuracy of the
experiment.
[12]
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Diagram
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