Canadian Association of Physicists Part A: Multiple Choice

1999 Prize Exam

Question 1
This is a three hour exam. National ranking and prizes The time dependence of the acceleration of a car is as
will be based on a student’s performance on both sections A shown. Which time corresponds to the maximum speed of
and B of the exam. However, performance on the multiple the car?
choice questions in part A will be used to determine whose a
written work in part B will be marked for prize consider-
ation by the National Committee. The questions in part
B of the exam have a range of difficulty. Please be careful t3 t4
to gather as many of the easier marks as possible before t1 t2 t
venturing into more difficult territory. In some cases an an-
swer to part (a) of a question is needed for part (b). Should
you not be able to solve part (a), assume a likely solution
and attempt the rest of the question anyway. No student is
expected to completely finish this exam and parts of each
(a) t1
question are very challenging.
(b) t2
Non-programmable calculators may be used. Please
be very careful to answer the multiple choice questions on (c) t3
the answer card/sheet provided to you and, most impor- (d) t4
tantly, write your solutions to the three written problems
on separate sheets as they will be marked by different peo- Question 2
ple in different parts of Canada. Good luck. Two identical loudspeakers are supplied with identical
sinusoidal signals. They are placed close to one another in a
Data room and it is noted that there are regions of increased and
decreased sound intensity in the vicinity of the speakers.
Speed of light c = 3.00 × 108 m/s
Which of the following actions will not change this pattern?
Gravitational constant G = 6.67 × 10− 11 Nm2 /kg2
Radius of Earth RE = 6.38 × 106 m (a) Moving one of the speakers.
Radius of Moon RM = 1.70 × 106 m (b) Changing the amplitude of the signal.
Mass of Earth ME = 5.98 × 1024 kg (c) Changing the frequency of the signal.
Mass of Moon MM = 7.35 × 1022 kg
(d) Replacing the air in the room with Helium gas.
Mass of Sun MS = 1.99 × 1030 kg
Radius of Moon’s orbit RE M = 3.84 × 108 m
Question 3
Radius of Earth’s orbit RE S = 1.50 × 1011 m
Acceleration due to gravity g = 9.81 m/s2 Two black objects of the same diameter, a sphere and
Fundamental charge e = 1.60 × 10− 19 C a disc, are placed in front of a uniform beam of light. The
Mass of electron me = 9.11 × 10− 31 kg plane of the disc is perpendicular to the light rays. The
Mass of proton mp = 1.673 × 10− 27 kg force acting upon them by the light is:
Mass of neutron mn = 1.675 × 10− 27 kg (a) zero
Planck’s constant h = 6.63 × 10− 34 Js (b) bigger on the disc.
Coulomb’s constant 1/4π²o = 8.99 × 109 Nm2 /C2 (c) bigger on the sphere.
Permeability of free space µo = 4π × 10− 7 N/A2
Speed of sound in air vs = 340 m/s (d) the same on both.
Density of air ρ = 1.2 kg/m3
Boltzmann constant k = 1.38 × 10− 23 J/K Question 4
Absolute zero T = 0 K, T = −273◦ C A 1 kg mass rests on the ground, at sea-level and at
Energy Conversion 1 cal=4.184 J the equator. What would its weight be if the earth were
Avogadro’s number NA = 6.02 × 1023 mol− 1 spinning ten times faster than is presently the case?
(a) 9.80 N
(b) 3.37 N
(c) 6.43 N
(d) 9.76 N
Canadian Association of Physicists Prize Exam 1999

Question 5 (a) remains less than g at all times.

An ideal Ammeter—a device to measure current in an (b) exceeds g at some point.
electrical circuit—should have an internal resistance which (c) becomes g just before hitting the table.
is, (d) is constant.
(a) zero.
(b) infinite. Question 10
Two 20 g worms climb over a 10 cm high, very thin,
(c) equal to the resistance of the circuit’s load.
wall. One worm is thin and 20 cm long. The other is fat
(d) equal to the internal resistance of the circuit’s power (but still thin compared to its length) and only 10 cm long.
source. What is the ratio of the potential energy of the thin worm
as compared to that of the fat worm when each is half way
Question 6 over the top of the wall?
A 100,000 kg aircraft drops a 1000 kg package of sup- (a) 1:1
plies over an arctic research station. What approximate
(b) 2:1
force is felt by the 100 kg pilot at the instant of the release?
(c) 2:3
(a) 1 N
(d) 1:2
(b) 10 N
(c) 100 N Question 11
(d) zero Suppose that the “Man Who Skied Down Everest”
went straight down an incline of 40◦ to the horizontal and
Question 7 subject to a coefficient of kinetic friction of 0.10. Starting
A converging lens forms an image of an object on a from rest, how long did it take him to reach a speed of
screen. The image is real and has twice the size of the 50 km/hr (Ignore air resistance)?
object. If the positions of the screen and the object are (a) 2.5 s
interchanged, leaving the lens in its original position, what (b) 9.0 s
is the new image size on the screen?
(c) 1.5 × 102 s
(a) Twice the object size. (d) 2.0 s
(b) Same as the object size.
(c) Half the object size. Question 12
(d) Can’t say as it depends on the focal length of the lens. A stone is thrown vertically downward from the edge
of a cliff with an initial speed of 10 m/s. Just before hitting
Question 8 the ground, it has a final speed of 30 m/s. If instead, the
stone were thrown horizontally outwards from the top of the
A bucket full of water is attached to the end of a rope cliff with the same initial speed as before, what final speed
and allowed to swing back and forth as a pendulum from would it have immediately before hitting the ground?
a fixed support. The bucket has a hole in its bottom that
allows water to leak out. How does the period of motion (a) 10 m/s
change with the loss of water? (b) 20 m/s
(a) The period does not change. (c) 30 m/s
(b) The period continuously decreases. (d) 40 m/s
(c) The period continuously increases.
Question 13
(d) The period increases to some maximum and then de- Two objects of equal mass, and heading towards each
creases again. other with equal speeds, undergo a head-on collision.Which
of the following statements is correct?
Question 9
(a) Their final velocities must be zero.
A pencil is placed vertically on a table top with its
(b) Their final velocities may be zero.
pointy end up and its sticky eraser end down. As it falls over
from this unstable position, its point of contact with the (c) Each must have a final velocity equal to the other’s
table remains stationary. During its fall, the acceleration initial velocity.
of its tip, (d) Their velocities must be reduced in magnitude.

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Canadian Association of Physicists Prize Exam 1999

Question 14 Question 18
A positive point charge +Q is placed at x = 0 and a A spherical capacitor is formed by two metallic and
negative point charge −Q is placed at x = a. The mag- concentric spherical shells. The capacitor is then charged
nitude of the electrostatic force between the two is F . If so that the outer shell carries a positive charge and the
another point charge +Q is paced at x = −a, the net force inner shell carries an equal but negative charge. Even if the
on the charge at the origin (x = 0) is, capacitor is not connected to any circuit, the charge will
eventually leak away due to the small conductivity of the
(a) 2F in the negative x-direction. material between the shells. What is the character of the
(b) F in the positive x-direction. magnetic field induced by this leakage current?
(c) 5F/4 in the positive x-direction. (a) Radially outwards from the inner shell to the outer
(d) 2F in the positive x-direction. shell.
(b) Radially inwards from the outer shell to the inner shell.
Question 15 (c) Circular field lines between the shells and perpendicu-
A simple circuit contains an ideal battery and a resis- lar to the radial direction.
tance R. If a second resistor is placed in parallel with the (d) No magnetic field is induced.
first,
Question 19
(a) the potential across R will decrease.
Which of the following has units of magnetic field?
(b) the current through R will decrease.
(a) kg C− 1 s− 1
(c) the current delivered by the battery will increase.
(b) kg A− 1 s− 1
(d) the power dissipated by R will increase.
(c) N C− 1 m− 1
(d) J A− 1 m− 1
Question 16
A positively charged insulator is brought near (but Question 20
does not touch) two metallic spheres that are in contact.
Near the geographic north pole is the magnetic north
The metallic spheres are then separated. The sphere which
pole which is, in fact, a south magnetic pole. At this point,
was initially farthest from the insulator will have,
the earth’s magnetic field points straight down. An electron
(a) no net charge. is projected southwards and horizontally from the magnetic
(b) a negative charge. north pole. The magnetic force on the electron will cause
it to be deflected to the,
(c) a positive charge.
(a) Up
(d) either a positive or negative charge.
(b) Down
(c) East
Question 17
(d) West
A uniform electric field is as shown. How many of
the labelled points have the same electric potential as the
Question 21
shaded point?
A diffraction grating has 300 “lines” per mm etched
E upon it. When light of wavelength 550 nm is normally
incident upon the grating, how many bright spots appear
on a screen a short distance away?
(a) 1
(b) 6
(c) 12
(d) 13
(a) 2
(b) 3 Question 22
(c) 4 A drop of oil (n = 1.4) is on a glass (n = 1.5) sheet
(d) 8 and is observed from directly above by reflected white light.

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Canadian Association of Physicists Prize Exam 1999

A number of circular constructive interference bands are Question 25

observed for each colour in the visible spectrum. Approx- In the film Armageddon, astronauts land on an aster-
imately how thick is the oil film where one observes the oid and are able to walk around “normally” due to the
third blue band from the outside edge of the drop. The gravitation of the large rock. Suppose that a spherical as-
wavelength of blue light may be taken to be λb = 450 nm. teroid has a mass M and a radius R. A spherical hole of
observer radius R/2 is excavated from the asteriod as shown. What
is the gravitational acceleration at a point on the surface of
the asteroid at a point just above the excavation?
air

oil
R
(a) 482 nm
(b) 675 nm
(c) 1125 nm
(d) 1350 nm

GM
Question 23 (a) R2
GM
A uniform, horizontal beam of light is incident upon (b) 2R 2
a prism as shown. The prism is in the shape of a quarter- (c) GM
8R 2
cylinder, of radius R = 5 cm, and has the index of refraction 7GM
(d) 8R 2
n = 1.5. A patch on the table top for a distance x from the
cylinder is unilluminated. The value of x is,

x
R

(a) 1.71 cm
(b) 2.24 cm
(c) 2.50 cm
(d) 5.00 cm

Question 24
Consider the following types of electromagnetic radi-
ation: radio waves, infra-red, visible light. Which of the
following statements are true?
(i) only radio waves can be used to transmit audio infor-
mation.
(ii) only infra-red radiation is emitted by very hot objects.
(iii) only visible light can be detected by humans.
(a) only i is true.
(b) only ii is true.
(c) only iii is true.
(d) None of the statements are true.

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Canadian Association of Physicists Prize Exam 1999

Part B (c) Remember that the constant force is always acting

upon the first bead. What is the time interval be-
Question 1 tween subsequent collisions between the first and sec-
ond beads? What then is the average speed of the first
Four charges, each of charge +e, are at the four corners bead? What is the speed of the “shock wave” that
of a square of side a = 1 cm. The four charges are fixed in travels down the wire?
place and are considered to be of point-size. Gravity plays
no role in this question. (d) If the whole process is repeated, but with collisions
+ + which are perfectly inelastic, what is the terminal speed
e p of the shock wave formed?
a
Question 3
a
From everyday experience and observations, estimate
the brightness of a full moon as compared to the noon day
p+ e+ sun. Brightness is defined as the luminous intensity as mea-
sured in units of power per unit area. To arrive at a rea-
(a) Sketch a diagram of the electric field due to this charge sonable numerical estimate, you will need to estimate some
system. physical parameters. It is essential that you explain the rea-
soning behind your estimates and include detailed drawings
(b) What is the net force acting upon one of the charges? and explanations to support your arguments.
(c) What is the electrostatic potential energy of this charge
system?
(d) Now suppose that two of the charges are protons and
the other two are positrons. A positron is the electron’s
anti-particle. It has the same mass as an electron but a
charge of +e. The four charges are suddenly released.
What are their speeds when they are a significant dis-
tance apart from one another?

Question 2
Suppose that we have a string of equally spaced beads
of mass m, their surfaces being separated by a distance
d, that are free to slide without friction on a thin wire.
Suppose that a constant force F acts on the first bead,
initially at rest, causing it to accelerate along the wire as
shown. This force acts only on the first bead and might be
created by a well directed, steady stream of air. The first
bead will collide with the second, which will in turn collide
with the third, and so on. Suppose that all collisions are
elastic.
F

1 d 2 3 4

(a) What is the speed of the first bead immediately be-

fore and immediately after its collision with the second
bead?
(b) What is the speed of the second bead immediately be-
fore and immediately after its collision with the third
bead?