SSC FSFCE Physics Paper 1 2011- QP.pdf

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MINISTRY OF EDUCATION

FIJI SEVENTH FORM CERTIFICATE EXAMINATION 2011

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

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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. Length Y of a box is measured to be 0.62 ±0.05 m. The value and the absolute uncertainty

for the length Y12 _is

A. 0.3 ± 0.031

B. 0.3 ± 0.3

C. 0.78 ± 0.2

D. 0.79 ± 0.03

2. Which of the following combinations of units have the dimensions of density?

A. kgm3

B. m3kg-1

C. kgm-3

D kgm2

3. A small rock having a mass of 50 g is thrown upward at a speed of U m/s. A second rock

having twice the mass of the first is thrown upward at a speed of 3 U m/s. The smaller rock reaches its maximum height in 2.0 s. The time for the larger rock to reach its maximum height is

A. 1.0 s

B. 2.0 s

8 A B C D

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4. A 10 N weight is supported by two strings as shown in the diagram below.

The tension T1 in the string on the left is given by T2 times

A. Cos 37o / sin 30o

B. Cos 30o / cos 37o

C. Sin 37o / cos 30o

D. Cos 37o/ cos 30o

5. A small mass moves along a circular path at a constant speed. Which of the following

relationships is not applicable to this motion?

A. V = (2πR)/T

B. Vf = Vi + at

C. F = ma

D. a = v2/R

6 . A large flywheel whose moment of inertia is 1.8 x 103 kgm2 stores 108 J of kinetic energy.

Its angular velocity in rad/s is

A. 2.36 x 102

B. 3.33 x 102

C. 1.05 x 103

D. 1.11 x 105

7. The acceleration of the 6 kg mass in the given frictionless system is

A. 10.0 m/s2

B. 5.0 m/s2

C. 2.0 m/s2

D. 1.6 m/s2

Turn Over

© MINISTRY OF EDUCATION, FSFCE 2011: PHYSICS.

2 kg

4 kg 6 kg

10 N

T1 T2

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8. In an experiment, several wires of the same length, L, and metal but different cross-sectional areas A, were chosen. For each wire, the resistance, R, and the cross-sectional area, A, were measured.

The relationship between R and A can be stated that

A. R is independent of A.

B. R is directly proportional to A.

C. R is inversely proportional to A.

D. there is a logarithmic relationship between R and A.

9. An electric toaster has a resistance of 8 Ω. When it is plugged into the outlet, a current of

15 A passes through the toaster. How much heat is produced in 5 minutes?

A. 1.8 x 103 J

B. 9.0 x 103 J

C. 2.9 x 105 J

D. 5.4 x 105 J

10. A battery is connected to a load whose resistance is 300 Ω.

The Є = 6.3 V but the voltage measured across its terminals VAB is only 6.0 V.

The internal resistance (r) of this battery is

A. 0.02 Ω

B. 10 Ω

C. 15 Ω

D. 300 Ω

11. When two electric charges are separated by a distance of 0.1 m, the force is F.

What is the magnitude of the force when the distance is increased to 0.3 m?

A. 3F

B. F

C. F/3

D. F/9

A B +

¯

r

Є

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12. The diagram below shows junction points in a circuit.

The unknown current and its direction is best represented by

A. B.

C. D.

\

13. Two identical metal spheres, P and R, are placed x meters apart. A third metal sphere Q is

placed at a point equidistant from spheres P and R as shown in the diagram below.

Spheres P and Q each carry a charge of +q coulombs and R carry a charge of –q coulombs.

Which arrow best represents the direction of the resultant force on Q?

A. B. C. D.

Turn Over

x m

x m x m

P R

Q 2A

4A

7A

I = ?

2A

4A

7A

2A

4A

7A 5A

9A 2A

4A

7A

2A

4A

7A

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14. A 24 V battery is connected to two capacitors as shown in the diagram.

The potential difference between the plates of the 3 µF capacitor is

A. 6 V

B. 12 V

C. 18 V

D. 24 V

15. A small object containing a charge Q produces an electric field at a point 3 m from

the object. The magnitude of the field is 16 x 104 N/C. The magnitude of Q is

A. 3.2 x 10-6 C

B. 1.6 x 10-4 C

C. 4.8 x 10 5 C

D. 9.0 x 10 9 C

16. In order for an object to move in a simple harmonic motion (SHM) when moved

from its equilibrium position, the object must

A. have inertia.

B. have weight with zero acceleration.

C. move in a circular path with zero acceleration.

D. experience a restoring force proportional to its displacement.

17. A sewing machine needle moves up and down with SHM of amplitude 3 cm and the

machine can sew 240 stitches per minute. The angular frequency (ω) in rad/s for the

sewing machine is

A. 8 π

B. 240 π

C. 480 π

D. 720 π

3µF

24 V

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18. The SI unit for the magnetic field B is tesla which is a derived unit. Which of the following combinations of units is equal to the tesla?

A. N/Cm

B. kg/C.s

C. J.s/C.m

D. N.s /C

19. Two long parallel wires carry equal currents in the same direction. The magnitude of the

force between the wires separated by distance, d is F. If the separation of the wires is

doubled, the force (F) between the wires is of magnitude

A. F/2 and attractive.

B. F/2 and repulsive.

C. F/4 and attractive.

D. F/4 and repulsive.

20. The period of oscillation of a mass suspended from a vertical spring is given by:

T = 2π k m

Which of the following graphs best represents the relationship between T and m for the

oscillating spring?

A. B. C. D.

21. A string fixed at both ends is set vibrating such that it has 3 nodes, one at either end and one

in the middle. If the string is 0.6 m long, what is the wavelength of the vibration?

A. 0.2 m

B. 0.3 m

C. 0.6 m

D. 1.2 m

Turn Over

m (kg) m (kg)

m (kg)

T2

(s2)

T2

(s2)

m (kg)

T2

(s2)

T2

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23 cm

22. The proton, q, shown in the diagram moves at a speed ν and enters a magnetic field, B of

magnitude 5.0 T.

B

x x x x x x x

+q → ν x x x x x x x x x x x x x x

The motion of the proton on entering the field B is

A. stationary.

B. linear and constant.

C. clockwise and circular.

D. anticlockwise and circular.

23.

In the diagram above, S1 and S2 are two wave sources generating waves of

wavelength 3 cm in a ripple tank. Point P is a point on the

A. first order nodal line.

B. second order nodal line.

C. first order antinodal line.

D. second order antinodal line.

24. The frequency of a photon of red light is 4.57 x 1014 Hz. The energy of the photon is

A. 3.03 x 10-19 J

B. 1.45 x 10-48 J

C. 6.990 x 1047 J

D. 6.90 x 10-19 J

~

29 cm

P S1

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25. Which of the following is affected by gravity?

A. x-rays

B. photons

C. electrons

D. gamma rays

26. Copper is a conductor of electricity because

A. no energy gaps exist.

B. large energy gaps of 3 eV to 6 eV exist.

C. electrons can jump band gaps of about 0.7 eV to 1 eV.

D. electrons move easily to higher energy levels and travel through the solid.

27. A charged particle enters a region with crossed uniform electric and magnetic fields.

The directions of the fields are indicated in the diagram below.

For the particles to pass straight through undeflected, the speed must be represented by

A. E + B

B. B / E

C. E / B

D. EB

28. An inductor of 0.5 H is connected to a 12 V supply and a steady current of 4.8 A is recorded

in the circuit. The time constant, τ is

A. 24 s

B. 12 s

C. 0.6 s

D. 0.2 s

Turn Over

+ + + + + + + + + +

x x x x x x x

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Use the diagram below to answer Questions 29 and 30.

29. The force exerted by the spring on the magnet is F, the weight of the magnet is W,

and the magnetic force exerted by the coil on the magnet is M.

Which of the following best represents the forces acting on the magnet?

F W M

A.

B.

C.

D.

30. If resistance X is increased, the

A. polarity of the coil changes.

B. current in the coil increases.

C. magnetic force acting on the coil increases.

D. magnetic force acting on the magnet decreases.

spring

coil

N S

X

Y K P Q

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SECTION B

[30 marks] The ten questions in this section are all compulsory.

Each question is worth 3 marks.

QUESTION 1

A high power line is supported by a tower with a guy wire as shown in the diagram below.

The force exerted by the power line is 500 N in a horizontal direction. The guy wire is fastened to the tower at a point 50 m above the ground. The tower weighs 507 N.

(a) Calculate the tension, T in the guy wire. (2 marks)

(b) Calculate the sum of the vertical forces exerted on the ground at the base

of the tower. (1 mark)

QUESTION 2

Leone, whose true weight is 950 N, is on an elevator that is descending from the

10th floor of a building. During a brief period, Leone observes that his weight

appears to be reduced to 700 N.

(a) Calculate the acceleration of the elevator. (2 marks)

(b) When the elevator brakes to a stop at the ground floor, it had a deceleration

of 3.0 m/s2. Calculate the apparent weight for Leone. (1 mark)

Turn Over

T

_{guy wire}

50 m

60º F= 500 N

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SECTION B (continued)

QUESTION 3

The diagram below shows a simple DC electric motor.

The square coil WXYZ is a single turn and has sides 2 cm long. The current through the

coil is 5.0 A. The field strength between the magnetic poles is 0.60 T.

(a) What is the magnitude and the direction of the magnetic force on the side XY

when it is in the horizontal position as shown in the diagram? (2 marks)

(b) The coil experienced a maximum torque when it is at the position shown in the

the diagram. Explain why. (1 mark)

QUESTION 4

A siren on a police car emits a sound which has a frequency of 2 000 Hz. The car is approaching a stationary observer at a speed of 100 km/hr.

[Speed of sound = 330 ms-1]

What frequency will the observer hears as the police car:

(a) approaches; (2 marks)

(b) moves away at 80 km/hr? (1 mark)

QUESTION 5

A pendulum of length 2.0 m and a mass of 5 kg swings with amplitude of 0.3 m. Calculate the:

(a) period (T); (1 mark)

(b) total energy of the SHM; (1 mark)

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QUESTION 6

An aircraft flies through a thundercloud at a height of 2 000 m. There are charge concentrations of + 40 C at height 3 000 m within the cloud and – 40 C at height 1 000 m above the ground.

Calculate the electric field (E) at the position of the aircraft. (3 marks)

QUESTION 7

A home-made capacitor may be constructed with two large pieces of aluminum foil separated by a somewhat larger sheet of waxed paper. Suppose the aluminum sheets are 20 cm x 30 cm, and the thickness of the waxed paper is 0.03 mm. Assuming the dielectric constant to be 2.6, calculate the capacitance of the assembly.

(3 marks)

QUESTION 8

The air wedge shown in the diagram is formed between two glass plates by putting a hair strand under one edge of the upper plate.

When the plates are illuminated from above with monochromatic light of wavelength of 500 nm, parallel fringes are observed having a spacing of 0.300 mm.

Calculate the thickness of the hair. (3 marks)

Turn Over

r+

r_

3 000 m

2 000 m

1 000 m

Height

⊕ ⊕ ⊕

q+

q–

ө ө ө ө

5 cm

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SECTION B (continued)

QUESTION 9

The Balmer series for the hydrogen atom corresponds to all electron transitions above the third energy levels to the second energy levels.

(a) Calculate the wavelength of the photon emitted in the Balmer series. (2 marks)

(b) Determine the shortest wavelength in the Balmer series. (1 mark)

QUESTION 10

Jone wants to convert a galvanometer of internal resistance 80 Ω with full scale deflection (fsd) of 1 mA to an ammeter that can read a maximum of 2 A.

(a) Calculate the resistance of the shunt.

(2 marks)

(b) Draw the circuit diagram showing how the shunt is connected.

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SECTION C

[40 marks] There are seven questions in this section. Answer any four questions.

Each question is worth 10 marks.

QUESTION 1

(a) A student holding a pair of objects sits on a pivoted stool which rotates

with negligible friction as shown in the diagram below.

The moment of inertia of the student, objects and stool is 2.25 kgm2.

The student is set in rotation with an initial angular speed of 1.7 rev/s with arms outstretched. As he rotates, he pulls the objects inward so that the new moment

of inertia of the system becomes 1.8 kgm2.

Calculate the new angular speed of the system in SI units. (2 marks)

(b) A copper wire has a square cross section of length 2.0 mm for each side.

It is 4.0 m long and carries a current of 10 A. The density of the free electrons is 8.3 x 1028 m-3 [Resistivity (ρ) of Copper = 1.7 x 10-8Ω m]

(i) Calculate the current density in the wire.

(ii) Determine the electric field strength of the wire.

(iii) Calculate the drift velocity of the electrons. (3 marks)

(c) Green light of wavelength 520 nm is shone on to a metal surface with work

function 2.00 x 10-19 J.

Calculate the:

(i) photon energy;

(ii) threshold frequency of the metal;

(iii) maximum velocity of the ejected electrons. (3 marks)

(d) (i) Describe what happens when unpolarised light passes through a

vertical axis polariser. (1 mark)

(ii) What happens when the light emerging from the polariser in (i)

passes through a horizontal polariser? (1 mark)

Turn Over

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SECTION C (continued)

QUESTION 2

(a) A solid cylinder of mass, m, and radius, r, starts from rest at a height, h, and rolls down a slope and then onto a horizontal surface as shown in the diagram below.

At the end of the slope it has a linear velocity (ν).

(i) Given that the rotational Inertia of the cylinder is I = ½ mr2 ,

show that the velocity, ν, at the bottom of the slope is:

ν = (2 marks)

(ii) Calculate v when h = 70 cm. (1 mark)

(b) The diagram below shows a combination of capacitors.

Calculate the:

(i) effective capacitance of the circuit;

3 / ) 4

( gh

h

C1 = 2µF C₃= 2µF

C4 = 3µF

C2 = 3µF

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(c) Among the natural frequencies of an air column in a pipe are the values

440 Hz, 660 Hz, 880 Hz and 1100 Hz; none of which is a fundamental frequency.

(i) Does the pipe appear to be open at only one end or open at both ends?

Explain your answer. (1 mark)

(ii) What is the fundamental frequency? (1 mark)

(iii) What is the frequency of the 4th overtone? (1 mark)

(iv) Assuming a wave velocity of 340 m/s, calculate the length of the

air column. (1 mark)

QUESTION 3

(a) The diagram shows a car on the banked turn of a test track. The speed of the car

is constant as this is the speed for which no frictional force is needed to keep the car in its circular path.

(i) Calculate the centripetal force and the angle, θ, required to keep a

2 000 kg car in a circular path of radius 157 m if the speed is 100 km/hr. (2 marks)

(ii) Make a force diagram showing all forces acting on the car as it travels

along a banked curve. (1 mark)

(b) A manufacturer decides to design a grating that will diffract the 3rd order of

spectrum of blue light (λ = 460 nm) through an angle of 60o.

Determine:

(i) the resulting separation between the slits on the grating;

(ii) the number of lines per metre needed to do this;

(iii) how the 3rd order angle will change, if a green light of wavelength

500 nm is used on the same grating.

(3 marks)

Turn Over

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(c) A mass m, of 1 kg is suspended from a light spring as shown in the diagram.

When a second 1 kg mass is added, the spring elongates 10 cm. The second mass is removed and the system is set into vibration with that remaining single 1 kg mass with an amplitude of 6 cm.

Calculate the:

(i) frequency of vibration; (2 marks)

(ii) maximum velocity of the vibrating mass; (1 mark)

(iii) maximum acceleration of the vibrating mass. (1 mark)

QUESTION 4

(a) Two cars, P and Q, each of mass 1 000 kg are travelling at right angles to each

other with velocities of 4.0 m/s and 6.9 m/s respectively as shown below. N

They collide at an icy intersection and move off locked together after the collision. Friction effects are to be neglected.

(i) Calculate the magnitude of the total momentum of both vehicles

before the collision. (2 marks)

P

Q

6.9 m/s

4.0 m/s spring

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(b) Use the diagram given below to answer the following questions.

(i) Using Kirchoff’s Current Law, write the equation relating

I1, I2 and I3 at junction F. (1 mark)

(ii) Using Kirchoff’s Voltage Law, write the equations for loop

ABCFA and loop FCDEF. (2 marks)

(iii) By solving the equations above simultaneously, find the

value of I1, I2 and I3. (2 marks)

(c) When the switch is closed in this circuit, a charge of 40 µC flows from the

battery to charge the capacitors.

(i) Calculate the capacitance (C) of the unknown capacitor. (2 marks)

Turn Over

16µF

8µF

C

5V

¯ + I1

I3

I2

8 V 1.2V

E F

A

B

C

D 2 Ω

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QUESTION 5

(a) NASA wants to place a satellite in a circular orbit 320 km above the surface

of the earth as shown in the diagram below.

In order to keep the satellite in orbit as intended, two calculations need to be performed to substantiate projections.

Calculate the:

(i) orbital speed of the satellite; (2 marks)

(ii) acceleration of the satellite. (1 mark)

[Re = 6.4 x 106 m, Me = 5.98 x 1024 kg)

(b) The diagram shows two points, A and B, in the vicinity of two point charges.

Point A is midway between the charges.

Calculate the:

(i) electric field at B; (2 marks)

M

ν

satellite

B

•

ө

⊕

A -40µC

+60µC

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(c) Red light of frequency, f = 4.8 x 10 14 Hz strikes a soap film. The speed of light is 3.0 x 108 m/s.

Find the:

(i) Wavelength, λ, of the light in air;

(ii) minimum thickness of the film to form an antinode;

(iii) minimum thickness for a dark fringe. (3 marks)

QUESTION 6

(a) The wheel and shaft shown below can rotate with negligible friction about

the dotted line axis. The shaft has diameter 6.0 cm and the weight of the mass, m, gives the string a tension of 1.5 N. The mass, m, falls 1 m in 20 seconds, starting from rest.

(i) What is the angular acceleration of the wheel? (2 marks)

(ii) Find the moment of inertia. (1 mark)

(b) A wave travelling through a string along the x-axis has the equation:

y = 0.06 sin (0.2x + 6t)

(i) State the direction and the amplitude of the wave. (1 mark)

(ii) Calculate the wavelength (λ) and the velocity (v) of the wave. (2 marks)

(iii) Write the equation for the wave travelling in the opposite direction. (1 mark)

Turn Over

m

T=1.5 N

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(c) A 120 Ω resistor, a 2 H inductor and a 5µF capacitor are connected in

series to a 15 V, 60 Hz AC supply.

Calculate the:

(i) impedance Z; (2 marks)

(ii) current I. (1 mark)

QUESTION 7

(a) The diagram below shows two masses connected by a light inextensible

string over a frictionless pulley. The coefficient of friction between the 7 kg mass and the plane is 0.27.

(i) Calculate the acceleration in the system. (2 marks)

(ii) Calculate T . (1 mark)

10 kg

7 kg

60º T1

T2

120Ω _{2 H} 5µF

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(b) An electron of charge (e = 1.6 x 10-19 C) and mass (me = 9.11 x 10-31 kg)

is accelerated between a pair of parallel plates 5 cm apart as shown.

(i) Calculate the electric field strength between the plates and state

the polarity of plate B. (2 marks)

(ii) What is the energy of the electron upon reaching plate A? (1 mark)

(iii) Calculate the speed of the electron upon reaching A. (1 mark)

(c) An artillery shell is fired with an initial velocity of 300 m/s at 55o above the

horizontal to prevent an avalanche on a mountain side as shown in the diagram below. The shell exploded 42.0 seconds after firing and hitting the target.

Calculate the:

(i) maximum height reached by the artillery shell;

(ii) range the shell would have travelled if there was no mountain;

(iii) height (h) of the explosion from the horizontal. (3 marks)

THE END

____________________________________

COPYRIGHT: MINISTRY OF EDUCATION, REPUBLIC OF THE FIJI ISLANDS, 2011.

250 V

5 cm

A B

55º

v = 300 m/s