EXAMINATION FOR ENTRANCE
SCHOLARSHIPS AND EXHIBITIONS
FEBRUARY 2014
PHYSICS
Time Allowed – 2 hours
The exam paper consists of three sections. There is no need for notebook or graph paper: all the
answers, including plotting and working out, should be given on the question sheet. In each
section, use the space below the question to work out the answers. There are two additional
pages at the end of the booklet for extra calculations or notes.
Section A is data analysis. Section B has five questions. Work out the answers after each question
and highlight your numerical answers by underlining or circling them. In your answers, do not
forget to indicate the units. Correct approaches, comments, ideas, methods and reasoning may be
marked even if the answer is not completely correct. Section C contains twenty multiple-choice
questions. Each question is followed by up to four potential answers, labelled with letters A to D;
only one of them is correct. Indicate your answer by clearly circling the letter of your choice. No
negative mark will be given for wrong answers. Each of Sections A and B is worth 20 marks;
section C is worth 40 marks.
Standard booklets of fundamental constants, provided by the school, can be used. However, the
list on the next page should be enough for answering the questions.
Please attempt to answer ALL questions
Calculators are allowed to be used.
1
Constants
Electron charge
e  1.60  10 19 C
Electron mass
me  9.11  10 31 kg
Gravitational constant
G  6.67 10 11 m3 kg 1s 2
Planck’s constant
h  6.63 1034 m 2 kg s 1
Speed of light
c  3  10 8 m/s
Gravitational acceleration
g  9.8 m/s 2
Sound speed in air
v  343 m/s
Conversions
Astronomical Unit
1 AU  1.5  1011 m
Ångström
1Å = 10–10 m
Day
1 day  86400 s
Electronvolt
1 eV  1.6  10 19 J
Absolute temperature
TK  To C  273.15
p (pico):
10–12
n (nano):
10–9
 (micro:
10–6
m (milli):
10–3
Formulas
Ideal gas equation:
PV  nRT
Gravitational force:
F
Kepler’s 3rd law:
r3 ~ T 2
Exponential decay with given half-life:
N t   N 0 2
Energy of electromagnetic wave:
E
2
Gm1m2
r2
hc


 hf
t

Section A
A toy bee of m  400 g total mass is suspended from a spring. When it is
pulled down and released, it starts to oscillate vertically. The distance of
the bee’s nose from the top of the spring, measured at sixteen different
times, is shown in the table below.
Time (s)
0
0.6 1.2 1.8 2.4 3.0 3.6 4.2
Distance (mm) 417 349 208 201 289 390 396 316
Time (s)
4.8 5.4 6.0 6.6 7.2 7.8 8.4 9.0
Distance (mm) 230 199 246 344 390 391 331 271
The first twelve measurements are plotted in the distance versus time graph below.
a) What uncertainty was assumed in the measurements, on the basis of which the error bars
have been added to the data points?
[1]
b) Plot the missing data points on the graph with error bars indicating the same uncertainty.
[2]
c) Connecting the data points, draw a suitable curve on the graph between t  0 and 9 s that
shows how the variation of displacement with time.
[2]
3
d) Measured from the top of the spring, what is the distance of the equilibrium position of the
bee’s nose?
[1]
e) By reading from the graph, estimate the amplitude, A, and the period, T, of the oscillation.
[2]
 1
f) Calculate the cyclic frequency, f    , and the angular frequency,   2 f  , of the
 T
oscillation.
[2]
g) Assuming simple harmonic motion, d t   d 0  A cos t  t0  , write up a function of time
for the displacement, by replacing the parameters d 0 , A ,  , and t 0 by suitable values, that
approximates the oscillatory motion of the bee’s nose.
[2]
h) Besides the displacement, the speed of the toy also oscillates between zero and a maximum
value.
h1) At which position is the bee’s speed zero?
[1]
h2) Estimate the maximum speed of the bee.
[1]


i) Work out the stiffness, k  m 2 , of the spring.
[1]
4
j) Using the displacement versus time function in question (g), work out the position of the
bee’s nose at t  9 s . Does that prediction agree with the last measured distance given in the
table?
[2]
k) Name three aspects of the oscillation that introduce uncertainty or error to the derived
characteristic parameters of the motion?
[3]
5
Section B
1
A box of mass m  40 kg is on the top of a table that can carry a maximum weight of
Fmax  500 N . The table, with the box on it is taken to an upper floor in an elevator. At what
rate does the elevator accelerate if the table top is found broken? (g = 9.8 m/s2)
[4]
2
A car is leaving a petrol station with zero initial speed at t0  0 and is moving on a long
horizontal straight road with constant acceleration a1  5 m/s 2 for four seconds. At t1  4 s ,
the driver suddenly changes the acceleration to a2  4 m/s 2 and keeps this new acceleration
until she arrives back at the petrol station. (The negative sign of a2 indicates that the
acceleration has changed to the opposite direction.)
a) When is the car the farthest from the petrol station?
b) When will the car get back to the petrol station?
[2]
[2]
3
Satellite A and satellite B are orbiting the Earth. The height of A above the surface of the
Earth is hA  0.2RE , while the height of B is hB  0.3RE , where RE is the Earth’s radius.
What is the ratio between the orbital periods of the two satellites, TA / TB  ?
[4]
4
The minimum light intensity that the eye of an owl is sensitive to is I min  5 1013 W/m 2 .
Supposed that the pupil of the owl’s eye can expand to a circle of diameter d  9 mm , at least
how many photons of wavelength   510 nm have to reach the owl’s eye per second so that
the bird can sense light? ( h  6.63 1034 Js , c  3 108 m/s )
[4]
5
The graph shows the mass of a radioactive material as a function of time.
What will be the mass of the material in t = 5 minutes?
6
[4]
Section C
1) How does the speed of a small free-falling object change during the fourth second of its
fall?
A) It does not change.
B) It increases by a factor of 4/3.
C) It increases by a factor of 9/4. D) It increases by a factor of 16.
2) According to our current knowledge, which of the following planets has satellites?
A) Mercury
B) Mars
C) Both
D) None of them
3) Andrew pushes, with a constant low speed, a sofa from one corner of a living room to
another on a horizontal surface. Then Barbara pushes the same sofa back to its original
position in the same way but with a constant high speed. Which of the following statements
is correct? Assume that friction does not vary with speed.
A) Andrew does more work than Barbara.
B) Andrew does the same amount of work as Barbara.
C) The power of Andrew’s action is more than the power of Barbara’s action.
D) The power of Andrew’s action is the same as the power of Barbara’s action.
4) What value of resistance can be made by using two resistors of 2 Ω and 3 Ω?
A) 1.2 Ω
B) 1.5 Ω
C) 2.5 Ω
D) 6 Ω
5) How much greater is the average angular speed of the minute hand of a clock than that of
the hour hand?
A) They are the same.
B) 6 times bigger
C) 12 times bigger
D) 60 times bigger
6) When point charge A is placed at distance l from point charge B, the force acting on point
charge A is F = 100 N. What force will act on A if we put point charge C halfway between A
and B, assuming that the charges of B and C are equal, QB  QC ?
A) F = 200 N
B) F = 300 N
C) F = 300 N
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D) F = 500 N
7) What is particle ‘X’ in the following nuclear process?
4
2
A) A neutron
He  94 Be  126 C  X
B) An alpha particle
C) A beta particle
D) A proton
8) Where is the Solar System relative to the Milky Way?
A) The Milky Way is part of the Solar System.
B) The Solar System is the nearest stellar system to the Milky Way.
C) The Solar System is between the centre and the edge of the Milky Way.
D) The Solar System is in the centre of the Milky Way.
9) A bicycle slows down from 20 m/s to 10 m/s . Its kinetic energy reduces…
A) by a factor of four.
C) by a factor of
2  1.4 .
B) by half.
D) by a factor of ten.
10) Is it possible for a proton to stay continuously at rest in a medium embedded in non-zero
homogeneous electric and magnetic fields which are constant over time?
A) Yes, if the electric and magnetic forces are the same and point in the opposite
direction.
B) No, as the only force acting on the proton is the electric force.
C) Yes, because electromagnetic forces act only on a moving particle.
D) No, as the electric and magnetic forces are always perpendicular to each other.
11) What can we find out from the frequency spectrum of an atom?
A) The energy differences between the electron states of the atom
B) The binding energy of the nucleus
C) The number of electrons in each energy state
D) The atomic mass
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12) A particle is performing a circular motion with period T. The radius of the circle is R.
What is its displacement over t  1.5T ?
A) d  1.41R
C) d  3.14R
B) d = 2R
D) d  4.71R
13) Can water be boiled at room temperature?
A) Yes, if the pressure is low enough.
B) Yes, if we gradually transfer a large enough amount of heat to it.
C) Yes, if it is clear H2O and the container is not touched or disturbed in any way.
D) No, it can only evaporate but not boil.
14) The unit of which physical quantity is the same as the unit of torque,   rF sin   ?
A) Pressure
B) Energy
C) Linear momentum
D) Power
15) Ten penguins are marching on a
straight, horizontal line in the snow at
the constant speed of v  0.2 m/s and
with the same distance of d  0.4 m
between them. Due to a sudden snow
storm, each of them instantaneously
slows down and continues their journey
with the constant speed of v  0.1 m/s .
What happens to their distance, d, due to going slower?
A) It decreases. B) It remains the same.
C) It increases.
D) It Decreases near the front of the row and increases at the back.
16) Consider an underground cave T  3 o C and a seaside beach T  28 o C. The relative
humidity is the same at the two places. The air at which place contains more water per unit
volume?
A) The cave.
B) The seaside beach.
C) The air at the two places contain the same amount of water per unit volume.
D) Rhere is not enough information to answer the question.
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17) The number of which particles increases during the nuclear fusion in the solar core?
A) Hydrogen atoms
B) Protons
C) Nucleons D) Helium molecules
18) Beryllium, 94 Be , has four protons, five neutrons and four electrons. A beryllium atom is
ionised by removing three of its electrons on-by-one. The removal of which electron requires
the largest amount of energy?
A) The first electron.
B) The second electron.
C) The third electron.
D) It is the same for all, as the required energy only depends on the kinetic energy of the
electrons.
19) During a thermodynamic process, the volume of a closed container expands from
V1  0.3 m 3 to V2  0.9 m 3 , while the temperature of the ideal gas in the container increases
from T1  35 o C to T2  70 o C . What happens to the gas pressure during the process?
A) The pressure decreases by about a factor of three.
B) The pressure increases by fifty per cent.
C) The pressure increases by a factor of six.
D) There is not enough data to answer the question.
20) The voltage in a circuit can be given by the following function of time:
V t   230 2 sin 100 t  ,
where t is measured in seconds. What is the maximum value the voltage takes?
A) 230 2 sin 100  V
B) 230 2 V
C)
10
2V
D) 230 V
Notes:
11
Notes:
12