MINISTRY OF EDUCATION
FIJI SEVENTH FORM CERTIFICATE EXAMINATION 2012
PHYSICS PAPER 1
Time Allowed: Three Hours
(An extra ten minutes is allowed for reading this paper.)
INSTRUCTIONS
1. Write all your answers in the Answer Book provided.
2. Write your Index Number on the front page and inside the back flap of the Answer Book.
3. If you require more paper, ask the supervisor for extra sheets. Tie these inside the Answer
Book at the appropriate places.
4. You may use a calculator, provided it is silent, battery-operated and non-programmable.
5. There are three sections in this paper. Sections A and B are compulsory. Note the
choices in Section C.
Note : Physical Data which may be useful during the examination is given on page 3 of the Answer Book.
SUMMARY OF QUESTIONS
Section Guidelines Total
Mark
Suggested Time
A
There are thirty multiple-choice questions.
All the questions are compulsory.
30 54 minutes
B There are ten questions.
All the questions are compulsory.
30 54 minutes
C There are seven questions.
Answer any four questions.
40 72 minutes
2.
SECTION A
[30 marks]The multiple-choice questions in this section are all compulsory. Each question is worth 1 mark.
INSTRUCTIONS FOR MULTIPLE – CHOICE QUESTIONS
1. In your Answer Book, circle the letter which represents the best answer. If you change your mind, put a line through your first choice and circle the letter of your next choice.
For example:
2. If you change your mind again and like your first answer better, put a line through your second circle and tick () your first answer.
For example:
3. No mark will be given if you circle more than one letter for a question.
1. A carpet is to be installed in a room of length 12.71 m and width 3.46 m. Find the area of the
room, retaining the proper number of significant figures.
A. 44.0m2
B. 43.98 m2
C. 43.9766 m2
D. 43.9m2
2. Which of the following is zero at the top of a projectile’s trajectory?
A. acceleration in the y-direction
B. y-component of the velocity
C. acceleration
D. velocity
3. A tennis player on serve tosses the ball straight up. While the ball is in free fall, its acceleration
A. increases.
B. decreases.
C. remains constant.
D. decreases then increases.
8 A B C D
8 A B C D
3.
4. A rocket of mass M moving with a constant velocity ν explodes and breaks into two
sections. After the explosion, one section of mass m of the rocket moves with a velocity of – ⱱ.
What is the velocity of the other section?
A. zero
B. m M M m ) ( C. m M M D. m M M
5. A disk is rotating with angular velocity of ω as shown in the diagram below.
The combined moment of inertia of the disk and the axle is I1. Now a second disk of
moment of inertia I2 is dropped onto the first and ends up rotating with it.
If the angular velocity of the second disk was initially zero, then the angular velocity of the combination is A. 2 1 I I B. 2 1 1 I 1 I C. 2 1 1 I I I D. 1 2 1 I I I Turn Over
© MINISTRY OF EDUCATION, FSFCE 2012: PHYSICS.
2
I
4.
6 . Four masses P, Q, R and S are placed in a line as shown below.
Which mass has the greatest moment of inertia about point X?
A. P
B. Q
C. R
D. S
7. The diagram below shows a satellite of mass m, in a circular orbit, at a height above
the earth’s surface equal to the radius of the earth.
The kinetic energy (Ek), potential energy (Ep) and total energy (ET) of the satellite, respectively is
8. In order for an object to move in simple harmonic motion (SHM) when it is displaced
from its equilibrium position, the object must
A. be suspended like a pendulum.
B. experience a gravitational force.
C. move in a circular path at a constant speed.
D. experience a restoring force proportional to its displacement.
Ek Ep ET
A.
R GmM
2 ─2Ek ─Ek
B.
R GmM
4 ─2 Ek ─Ek
C.
R GmM
4 ─ R
GmM
2 Ek
D.
R GmM
2 ─ R
GmM
2
0
satellite of mass, m
Earth of mass, M
R R
X
P 2 kg Q 1 kg R 0.5 kg S 0.25 kg
5.
9. A 6 kg block rests on a plane inclined at 30
º
to the horizontal. The coefficient offriction of the plane is 0.4.
The arrows in the diagram represent force vectors associated with the block. The magnitude of the frictional force between the block and the plane is
A. 30 N
B. 12 N
C. 30 N
D. 12 N
10. A wheel of mass 12.0 kg and radius 0.35 m, rolls down a slope from a height of
5 m above the lowest point P.
At P the wheel is found to have 294 J of translational kinetic energy with a speed of 7 ms1. The rotational kinetic energy of the wheel is
A. 906 J
B. 600 J
C. 306 J
D. 294 J
11. Which of the following statements relating to the band theory of conduction in
solids is not true?
A. The valence band of conductors is partially filled.
B. The valence band of semi-conductors is completely filled.
C. Resistivity decreases with the temperature of conductors.
D. Resistivity decreases with the temperature of semi- conductors.
Turn Over
© MINISTRY OF EDUCATION, FSFCE 2012: PHYSICS.
P
30
º
PS
R 6 kg
6.
12. A block on the end of a spring is pulled to position x = A and released. Through
what total distance does it travel in one full cycle of its motion?
A. A/2
B. A
C. 2A
D. 4A
13. A fire truck travels at 30 ms towards a person waiting at a bus stop. The truck 1 produces a siren of frequency 500 Hz.
Which of the following frequencies does the person hear?
A. 42 Hz
B. 50 Hz
C. 458 Hz
D. 550 Hz
Use the information given below to answer Questions 14 and 15.
A circuit consists of a battery, a 6 Ω resistor, a switch, a voltmeter and an ammeter connected as shown below.
When the switch is open, the voltmeter reads 12 V. When the switch is closed, the ammeter reads 1.5 A.
14. What is the internal resistance of the battery?
A. 2 Ω
B. 4 Ω
C. 6 Ω
D. 8 Ω
15. What reading will the voltmeter show when the switch is closed?
A. 3 V B. 6 V C. 9 V D. 12 V
V
r
S A 6 Ω
7.
16. A charged sphere of value 3.2 C is placed 200 cm away from an object.
The magnitude of the electric potential experienced by the object is
A. 144 V
B. 1.44 x1010V
C. 1.44 x104V
D. 1.44 x108V
17. John’s favourite AM radio station has a frequency of 1.2 x 106 Hz.
The wavelength of the electromagnetic waves transmitted is
A. 275 m
B. 250 m
C. 400 m
D. 3 600 m
18. A parallel plate capacitor of capacitance C, is charged by connecting it to a battery.
The battery is now disconnected and the plates are moved further apart.
Which of the following would decrease?
A. charge on the plates
B. capacitance of the capacitor
C. energy stored in the capacitor
D. electric field between the plates
19. Which of the following is a unit for electric potential?
A. N.C.m
B. N.C–1m
C. N.C.m–1
D. N.C–1 m–1
20. Two identical point charges d metres apart experience a mutual electrostatic force
of F Newtons. After the separation distance is changed, the force between them is now 4F. In terms of d, the new separation distance is
A. d/2
B. d
C. 2/d
D. 4d
Turn Over
8.
Use the information given below to answer Questions 21 and 22
Yellow light from a sodium lamp (λ = 5.893 x 10–7 m) is directed at a sheet of glass with a grating of 2 000 lines per metre. When a screen is placed 1.0 m away, a series of fringes are seen.
21. The two optical phenomena responsible for causing such fringes are
A. reflection and refraction.
B. reflection and diffraction.
C. interference and diffraction.
D. interference and refraction.
22. What would be the effect on the spacing between the fringes if the grating had only
1 600 lines per metre?
A. The spacing would be bigger.
B. The spacing would be closer.
C. The spacing would not change.
D. There would be no fringes seen on the screen.
23. A 12.6 V battery is in series with a resistance of 0.350 and an inductor.
What is the current after one time constant?
A. 36 A
B. 22.75 A
C. 13.32 A
D. 4.41 A
24. A solenoid of N turns in a length L is energised by current I. If the solenoid length, turns, radius and current are all doubled, the magnetic field within the new solenoid compared to that in the old will be
A. one-quarter.
B. one-half.
C. the same.
9.
Use the information given below to answer Questions 25 and 26.
The diagram shows a narrow beam of yellow light at near-normal incidence to a thin air-layer between two glass slides. At point A, some of the light is reflected and the rest is transmitted.
25. Consider the following statements about the reflected waves from A and from B:
I. The light reflected at point A undergoes a change of phase of half a cycle.
II. The light reflected at point B undergoes a change of phase of half a cycle.
III. At point B there is a half cycle phase difference between the reflected and
transmitted light.
Of these three statements, only
A. I is true.
B. II is true.
C. I and II are true.
D. II and III are true.
26. The yellow light has a wavelength λ in air and the refractive index of the glass for the
yellow light is n. If the reflected light waves from points A and B entering the observer’s eye are in phase, then the least possible thickness of the air-layer is
A.
4
B.
n
4
C.
4
n
D.
2
Turn Over
© MINISTRY OF EDUCATION, FSFCE 2012: PHYSICS. Glass
A
B Air
10.
27. An energy level diagram with some of the energy transitions possible for a hydrogen
electron is shown below.
Which transition produces the photon with the longest wavelength?
A. I
B. II
C. III
D. IV
Use the information given below to answer Questions 28 to 30.
The diagrams show a square loop of copper wire of side length L, moving at a constant velocity, into a uniform magnetic field B, directed into the page.
28. The time taken, t for the loop to move between the two positions shown in the diagrams
is given by
A.
L
t
B.
L
t
C. t L
D.
L
2
t
I II
III IV
Magnetic field B
LOOP LOOP
11.
29. The change in the magnetic flux,
ø
through the loop during the time t that it movesbetween the two positions shown in the diagrams is given by
A.
ø =
L B
B.
ø =
2L B
C.
ø =
BL 2D.
ø
=
B L2
30. The voltage induced in the loop is given by
A.
ɛ
BB.
ɛ
BLC.
ɛ
L B
D.
ɛ
BL
Turn Over
12.
SECTION B
[30 marks]The ten questions in this section are all compulsory. Each question is worth 3 marks.
QUESTION 1
A flywheel, initially at rest, accelerates uniformly at 3.0rads2for 20 seconds.
Find the following:
(a) the angle it turns through; (1 mark)
(b) the linear acceleration of a point 12 cm from the centre of the wheel; and (1 mark)
(c) the angular velocity after 20 seconds. (1 mark)
QUESTION 2
The best leaper in the animal kingdom is the puma which can jump to a height of 12 feet (ft) when leaving the ground at an angle of 45º.
(a) With what speed, in SI units, must the animal leave the ground to reach
that height? (1 ft = 0.3048 m) (2 marks)
(b) What corresponding horizontal distance does this leap cover? (1 mark)
QUESTION 3
A certain solenoid consists of 100 turns of wire and has a length of 10.0 cm.
(a) Find the magnitude of the magnetic field inside the solenoid when it carries a
current of 0.500 A. (1 mark)
(b) What is the momentum of a proton orbiting inside the solenoid in a circle with
a radius of 0.020 m? (2 marks)
13.
QUESTION 4
The diagram given below shows a combination of capacitors connected to a power supply.
(a) Determine the equivalent capacitance for the combination. (1 mark)
(b) What is the total charge flowing in the circuit? (1 mark)
(c) Determine the voltage across the 3 μF capacitors. (1 mark)
QUESTION 5
A fine iron wire 20 cm long is connected to a battery as shown in the diagram.
The potential difference between the two ends of the wire is 3.0 Volts.
(a) What are the magnitude and direction of the electric field inside the wire? (2 marks)
(b) What is the potential difference between points A and B that are separated
by 4 cm? (1 mark)
QUESTION 6
(a) A spring with constant k = 475 N/m stretches 4.50 cm when an object of mass
25.0 kg is attached to the end of the spring.
Find the acceleration of gravity at this location. (2 marks)
(b) One of the uses of polaroid is in polaroid glasses. How do polaroid glasses
reduce the effect of the glare of the sun? (1 mark)
Turn Over
© MINISTRY OF EDUCATION, FSFCE 2012: PHYSICS.
− +
μF 3
μF 3
μF
6 6 μF
12 V
20 cm
14.
SECTION B (continued)
QUESTION 7
The equation of a travelling wave is given as:
(
)
0.4 0.02
2 cos
0.04 t x
y
Calculate the:
(a) period T, of the wave. (1 mark)
(b) wavelength. (1 mark)
(c) speed of the wave. (1 mark)
QUESTION 8
A milliammeter reads 1 mA full scale and has a resistance of 100 Ω. This is to be converted to a voltmeter reading 10 V full scale.
(a) Draw a circuit diagram showing how the conversion can be done using
a resistor. (2 marks)
(b) Calculate the value of the resistance required. (1 mark)
QUESTION 9
(a) Give one application of electrically tuning an AC circuit to resonance. (1 mark)
(b) State the relationship between the resonant frequency fo and the values of
capacitance C and the inductance, L in the circuit. (1 mark)
(c) Calculate the resonant frequency in an AC circuit with a 100 μF capacitor and a
20 mH inductor in series. (1 mark)
QUESTION 10
Calculate the wavelength of the light emitted when an electron falls from energy
level of -6.06 x 10-20J to an energy level of –8.73 x 10-20J. (3 marks)
15.
SECTION C
[40 marks]There are seven questions in this section. Answer any four questions. Each question is worth 10 marks.
QUESTION 1
(a) In the diagram given below, all surfaces are frictionless.
Calculate the following:
(i) acceleration of the system; (1 mark) (ii) T1 ; and (1 mark)
(iii) T2. (1 mark)
(b) In the diagram given below, the values of the resistors in branches EB and EC
are unknown. The ammeter in branch EB, however reads zero.
(i) Determine the resistance, R of the branch EC. (1 mark)
(ii) Calculate the current supplied by the battery. (1 mark)
(c) A loudspeaker of variable frequency is put close to one end of a pipe 80 cm
long that is open at both ends. The first resonance is heard at 210 Hz.
Calculate the:
(i) speed of sound in air. (1 mark)
(ii) next two resonant frequencies. (1 mark)
Turn Over
© MINISTRY OF EDUCATION, FSFCE 2012: PHYSICS
•
B
1Ω 1.5Ω
2Ω 2Ω
10V
A C
R A
E
D T1
T2
20 kg
4 kg
16.
SECTION C (continued)
(d) The aerial of a radio receiver is connected as shown. The capacitor is varied to tune
the circuit to 500 kHz if the radio wave induces 0.10 mV between the aerial and the ground.
Find the:
(i) necessary value of the capacitor. (2 marks)
(ii) rms current in the circuit at resonance. (1 mark)
QUESTION 2
(a) Two objects A and B are moving as indicated in the diagram below.
Before After
Determine the angleθ, which the path of the objects makes with the x – axis
after the collision. (3 marks)
0.10 mV 30 mH
150
c
Ground
θ
2.0 kg 3.0 ms-1
ⱱ
•
30º
1.0 kg
6.0 ms-1 60º
P
A
B
A
+10
0
-10
B 17.
(b) The wave shown below travels to the right at a frequency of 10 Hz.
(i) What is the speed of the wave? (1 mark)
(ii) Which way is point B moving at the instant shown? (1 mark)
(iii) Write an equation for the travelling wave. (1 mark)
(c) In a particular wire, electrons move with a drift velocity of 0.5 mm s–1 through a
cross-sectional area of 4 mm2. There are 1029 electrons in each m3 of wire.
The wire is 12 mm long.
(i) What is the total number of electrons carried by the wire? (2 marks)
(ii) Calculate the size of the current. (1 mark)
(iii) Calculate the current density in the wire. (1 mark)
QUESTION 3
(a) A toy train consists of eight identical carriages of mass 0.5 kg and a locomotive
of mass 1.00 kg. When it is started, it accelerates from rest to 1.00 ms–1 in 0.50 s.
(i) What is the magnitude of the train’s acceleration? (1 mark)
(ii) What is the size of the unbalanced force on the last carriage? (1 mark)
(iii) What force does the last carriage exert on the rest of the train in front
of it? (1 mark)
Turn Over
© MINISTRY OF EDUCATION, FSFCE 2012: PHYSICS.
0.2 0.4 0.6 0.8 x (m) position
18.
SECTION C (continued)
(b) In the diagram below a thin beam of white light shines on to a diffraction grating.
A scientist wants the violet light of wavelength 420 nm to be diffracted into
apparatus X and the red light which has a wavelength of 650 nm to be diffracted
into apparatus Y.
(i) What slit spacing must the grating have to diffract violet light into
apparatus X in first order? (1 mark)
(ii) At what angle must apparatus Y be placed to receive red light diffracted
in first order? (1 mark)
(c) The graph shown below is of the stopping voltage V versus the filter frequency f for
a photoemissive cell.
(i) Determine the value of the Planck’s constant from the graph.
Express your answer to 3 significant figures. (2 marks)
(ii) What is the threshold frequency of the light? (1 mark)
10º θ
Violet
X
Y Red
(x1014 Hz)
Graph of stopping voltage versus the filter frequency for a photoemissive cell
0 0.4 0.8 1.2 1.6
─0.4 ─0.8 ─1.2 ─1.6
2.0 4.0 6.0 8.0
V
19.
(d) A rectangular loop of dimensions 7 cm and 14 cm is oriented in a magnetic
field of strength 0.50 T at an angle of 35
º
. The current in the loop is 2.5 A.Find the magnitude of the torque at that instant. (2 marks)
QUESTION 4
(a) A mountain bike athlete wants to investigate whether the rotational inertia of the
wheels has much effect on the motion of the bike.
(i) The mass of a bike wheel is measured to be m = 1.4 kg and its radius is
measured at r = 0.35 m. Use I= mr2to calculate the wheel’s rotational
inertia. (1 mark)
(ii) The athlete then rides the bike at a measured speed of 2.5 ms-1.
Calculate the angular speed of the wheels. (1 mark)
(iii) The total mass of the bike and the rider is recorded as 82 kg.
Calculate the translational kinetic energy of the bike and its rider. (1 mark)
(iv) What can you conclude about the effect of the wheel’s rotational inertia
on the bike’s motion? (1 mark)
(b) A wooden ring of mean diameter 0.1 m is wound with a closely spaced toroidal
winding of 300 turns.
What is the strength of the magnetic field at a point on the mean circumference of the ring when the current in the windings is 0.5 A and determine the
magnetic field strength outside the toroid. (2 marks)
(c) In the diagram given below, the charge at A is 6 x 10–6 C and at B is 8 x 10–6 C. The point P is equidistant from A and B, the distance being 0.1 m.
Calculate the:
(i) electric field strength at P. (2 marks)
(ii) electric potential at P. (2 marks)
Turn Over
© MINISTRY OF EDUCATION, FSFCE 2012: PHYSICS.
B
A
0.1 m P
0.1 m
+
20.
SECTION C (continued)
QUESTION 5
(a) A carnival ride has cars that move at constant speed in a vertical circle of
radius 18 m.
(i) What must the angular velocity be so that a 100 kg passenger
will be "weightlessʺ when at the highest point, P? (2 marks)
(ii) What will be the passenger’s apparent weight at point Q? (1 mark)
(b) The diagram given below shows a uniformly charged sphere with lines of force
radiating from it. Points X and Y lie on an imaginary spherical surface of radius r1
which is concentric with the charged sphere.
(i) If the charge on the sphere is 0.2 μC and the radius r1 is 0.02 m,
what is the magnitude of the force on a charge of 0.1 μC placed at X? (2 marks)
(ii) How much work is done if the charge of 0.1 μC is moved along the
spherical surface from X to Y? (1 mark)
(iii) What is the potential difference between points X and Y? (1 mark)
(c) A diffraction grating having 5 000 lines per centimetre was used to find the
wavelength of a monochromatic light source. The second order maximum for a certain yellow light was formed at an angle of 30º from the central maximum.
(i) Find the wavelength of the light source. (2 marks)
(ii) Altogether, how many maxima will be formed with this light? (1 mark)
Q P
μ=R
r = 18 m
r1
Y
• Y
X
+ + + +
+ + +
21.
QUESTION 6
(a) A small mass vibrating with SHM has a velocity of 0.5 ms-1 as it passes
through its equilibrium position – the midpoint of the motion.
(i) What is the velocity of the mass at its maximum displacement? (1 mark)
(ii) If the amplitude of the vibration is 5 cm, what is the period? (1 mark)
(b) Two parallel wires are 10.0 cm apart, and each carries a current of 10.0 A.
If the currents are in the same direction,
(i) find the force per unit length exerted on one of the wires by the other.
Are the wires attracted to or repelled by each other? (2 marks)
(ii) sketch a simple diagram showing the cross-section of the conductors
in (i) and the pattern of the magnetic field around them. (1 mark)
(c) The escape speed, of a body from a planet is usually given as
R 2GM
where M is the planet’s mass, R is its radius, and G, the universal gravitation constant.
(i) If the weight of a mass is the same as the gravitational attraction to a
planet, show that the escape velocity at the earth’s surface can be given by
2gR
where g is the gravitational field strength on the planet’s
surface. (2 marks)
(ii) Hence, calculate the escape velocity of a mass from earth, of radius
6 400 km. (1 mark)
(iii) What would be the escape speed of a 500 kg satellite and a 1000 kg
satellite at a given radius? Explain your answer. (1 mark)
(d) The diagram, part of the emission spectrum of hydrogen, shows some lines
from the Balmer Series.
Give the letter of the line with the lowest frequency and the shortest
wavelength. (1 mark)
Turn Over
© MINISTRY OF EDUCATION, FSFCE 2012: PHYSICS.
a b c d e
22.
SECTION C (continued)
QUESTION 7
(a) The circuit given below shows resistors and two sources in a multi-loop.
Using Kirchoff’s laws,
(i) write an equation linking I1, I2, and I3 at point C. (1 mark)
(ii) write equations representing Voltage drops around loops:
1. ABCFA (1 mark)
2. CDEFC (1 mark)
(iii) find values of I1, I2, and I3.
Use equations from (i) and (ii). (2 marks)
(b) A SHM has the equation )
4 (4t
6.8
sin y
(i) What is the initial phase angle, Ɵ? (1 mark)
(ii) Calculate the velocity at time 0 sec. (2 marks)
(c) A 10 Ω resistor, 100 μF capacitor and 20 mH inductor are connected in series
to the 50 Hz mains voltage supply.
Draw the circuit diagram described above using the correct electrical symbols. (2 marks)
THE END
____________________________________ COPYRIGHT: MINISTRY OF EDUCATION, REPUBLIC OF FIJI, 2012.
B C D
8
4
4
24V
8 V
A
F E
