SSC FSFE Physics Paper 1 2009-QP.pdf

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FIJI SEVENTH FORM EXAMINATION 2009

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. A density of 19.3 gcm-3 is the same as A. 1.93 x 10-2 kgm-3

B. 1.93 x 10-1 kgm-3 C. 1.93 x 104 kgm-3 D. 1.93 x 106 kgm-3

2. A sphere has a volume of 0.8 m3. A second sphere has half the radius of the first. The volume of the second sphere is

A. 0.1 m3 B. 0.2 m3 C. 0.4 m3 D. 1.6 m3

3. Newton’s Universal Law of Gravitation is an “inverse-square” law. By what factor does the gravitational force between the earth and a satellite change if the radius of orbit of the satellite is tripled ?

A. 9 1

B. 3 1

C. 3

D. 9

© MINISTRY OF EDUCATION, FSFE 2009 : PHYSICS.

8 A B C D

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Refer to the information given below to answer Questions 4 and 5.

The velocity – time graphs below are of a car A already travelling at a constant speed of 24 ms-1 and a car B which starts from rest and uniformly accelerates at 4 ms-2 to a speed of 30 ms-1 in 10 s, after which it travels at this constant speed of 30 ms-1.

4. What is the value of time t1, when the cars are at the same speed ? A. 96.0 s

B. 25.0 s C. 7.5 s D. 6.0 s

5. How long does car B take to catch up to car A ? A. 96.0 s

B. 25.0 s C. 7.5 s D. 6.0 s

6. A 1.0 kg bird is flying horizontally overhead at 1.5 ms-1 when it is hit by a bullet of mass 0.01 kg fired vertically upwards at 100 ms-1. If the bullet is lodged in the bird, the speed of the bird and the bullet immediately after the impact is approximately

A. 1.5 ms-1 B. 1.8 ms-1 C. 10.1 ms-1 D. 101.5 ms-1

Turn Over

© MINISTRY OF EDUCATION, FSFE 2009 : PHYSICS. B

A 30

24

0 t1 10

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Refer to the information given below to answer Questions 7 and 8.

A 3.0 kg mass attached to a spring with spring constant 300 Nm-1, undergoes simple harmonic motion with amplitude 0.4 m.

7. The total mechanical energy of the simple harmonic oscillator is A. 360 J

B. 120 J C. 24 J D. 12 J

8. The graph of the speed of the mass as a function of position is

A B

C D

9. A 500 N weight is held suspended in equilibrium by two cables, T1 and T2, as shown in the diagram below.

The value of tension T1 is about

A. 301

B. 500

C. 626

D. 831

x x

37º

500 N

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10. A 10 kg mass attached to a spring is dragged at constant speed up a rough surface whose coefficient of friction is 0.3. The extension of the spring is constant at 8 cm. The surface is inclined at 10º as shown below.

The spring constant equals

A. 08 . 0 10 Sin 100 10 Cos 30 B. 08 . 0 10 Sin 100 10 Cos 30 C. 08 . 0 10 Cos 30 10 Sin 100 D. 08 . 0 10 Sin 100 10 Cos 30

11. A 0.25 m long fan blade rotates at 10 revs/min. Its angular speed in rads-1 at a point half-way along the blade is

A. 9 16 B. 9 2 C. 6 D. 12

12. The escape speed of a mass X from a planet depends only on both A. the mass of X and the radius of X.

B. the mass of X and the mass of the planet. C. the mass of the planet and the radius of X.

D. the mass of the planet and the radius of the planet.

Turn Over

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13. A car delivers 30 hp to its wheels when moving at the constant speed of 22 ms-1. If 1 hp = 746 watts, then the resistance force on the car at this speed is nearest A. 840 N

B. 1 020 N C. 18 600 N D. 410 000 N

14. A satellite is held in circular orbit by a 2 000 N gravitational force between it and a planet. Each time the satellite completes one orbit of circumference 80 000 km, the work done on it by gravity is

A. 0

B. 1.6 x 106 J C. 1.6 x 1011 J D. 6.4 x 1011 J

15. A mass of 0.3 kg at the end of a 25 cm long string is swung in a vertical circular path. The angular speed at the top of the path is 12 rads-1.

According to the information given, the tension in the string at the top of the circular path is approximately

A. 83 N

B. 18 N

C. 16 N

D. 8 N

16. For an ideal gas of a given mass, it is observed that the volume increases while the pressure is kept constant. Which of the following is true of the gas molecules under these

conditions ?

A. the average kinetic energy decreases

B. the average kinetic energy remains constant C. the average kinetic energy increases

D. nothing can be determined about the kinetic energy

17. Two waves of equal and constant frequency travel in the same medium and undergo constructive interference. The phase difference between the waves would be

A. 0º B. 90º C. 180º D. 270º

0.3 kg 12 rads-1

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18. Waves travel at 8 ms-1 along a stretched string. The end of the string is vibrated up and down once every 2.0 s. What is the wavelength of the waves that travel through the string ? A. 3.0 m

B. 5.3 m C. 6.0 m D. 16.0 m

Refer to the information given below to answer Questions 19 – 21. A sinusoidal wave is represented by y (x, t) = 0.4 cos (6x – 10t) metres.

19. The wavelength of the wave is A. 0.4 m

B. 1.67 m C. 1.59 m D. 1.05 m

20. The frequency of the wave is A. 0.4 m

B. 1.67 m C. 1.59 m D. 1.05 m

21. The maximum displacement of a particle of the medium from its equilibrium position is A. 0.4 m

B. 1.67 m C. 1.59 m D. 1.05 m

22. A pure inductor of 0.5 H is connected to a 240 V, 50 Hz mains supply. The reactance of the circuit is

A. 25 B. 210 C. 157 D. 235

Turn Over

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The diagram given below shows an electrical circuit. Use the circuit to answer Questions 23 and 24.

23. The total resistance of the circuit is A. 1.71

B. 3.71 C. 7.71 D. 9.71

24. The voltage drop across the 4 resistor is about A. 12.0 V

B. 6.8 V C. 5.5 V D. 8.0 V

25. The graph representing the relationship between the inductive reactance (XL) and the angular frequency ( ) is

A B

C D

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3

12 V

XL XL

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26. Resonance in a series RLC circuit occurs when A. XL > XC

B. XL < XC C. XL = XC D. Impedance = XC

27. Which of these laws is Faraday’s Law of Induction ? A. E.dl

B. B.dl C. E.dA D. B.dA

28. The forces acting on two parallel conductors carrying identical currents in the same direction are

A. attractive and different. B. repulsive and equal. C. attractive and equal. D. repulsive and different.

29. A long straight wire carrying a current of 3 A generates a magnetic field. The strength of the field at a point 4 cm from the conductor is

A. 2 x 10-5 T B. 3 x 10-5 T C. 4 x 10-5 T D. 1.5 x 10-5 T

30. When a charged particle mass moves freely in a circular path in the presence of a constant magnetic field (B), perpendicular to the particle velocity, its kinetic energy

A. becomes zero. B. remains constant. C. increases.

D. decreases.

Turn Over

O O

O

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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 river flows due east at 3.0 ms-1. A boat crosses the 300 m wide river, its speed relative to calm water being a constant 10 ms-1.

(a) If the boat steers due north relative to the water, how far downstream does the

boat move by the time it reaches the other bank ? (2 marks)

(b) If the boat is to cross along a line perpendicular to the river banks, at what angle

upstream from the bank should it steer ? (1 mark)

QUESTION 2

A 9.0 kg hanging weight is connected by a light string over a smooth pulley to a 5.0 kg block sliding on a flat table. If the coefficient of sliding friction is 0.20, calculate the

tension in the string. (3 marks)

QUESTION 3

(a) At lift off, the engines of a rocket used 13 000 kgs-1 of fuel and exhausted the combustion products at 2 900 ms-1. Calculate the total upward thrust provided

by the engines. (2 marks)

(b) A car speeds round a 52 metre radius curve banked at 45º. Calculate the speed of the car, if no friction is required between the road and the tyres to prevent the car

from slipping. (1 mark)

© MINISTRY OF EDUCATION, FSFE 2009 : PHYSICS. 5 kg

9 kg T

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QUESTION 4

(a) A 800 N painter stands on a 4.0 m scaffold, supported by vertical ropes at each end.

If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is

the value of the tension in the rope nearest the worker ? (2 marks)

(b) Two loud speakers are placed side by side and driven by the same source at 500 Hz. A listener directly infront of the speakers hears the loudest sound at the point where he stands. How far must one of the speakers be moved towards the

listener to repeat the condition of loudest sound at the listener’s ear ? (1 mark)

QUESTION 5

A solid sphere of 4.0 kg mass and of radius 0.12 m starts from rest at the top of a 2.4 m high ramp. For the sphere, the moment of inertia is given by 0.4 MR2. Calculate the

speed of the sphere when it reaches the bottom of the ramp. (3 marks)

QUESTION 6

A ray of light in air enters crown glass at an angle of incidence of 30º. The crown glass has a refractive index of 1.52.

(a) Calculate the speed of the light in crown glass. (1½ marks) (b) What is the angle of refraction in the glass ? (1½ marks)

QUESTION 7

A bullet train approaches a stationary observer on a platform at a constant speed of 40 ms-1. The train sounds its horn as it nears the platform, producing sound of 500 Hz frequency.

(a) What is the wavelength of the waves that arrive at the observer ? (1½ marks)

(b) What is the frequency of the sound from the horn as heard by the observer ? (1½ marks)

Turn Over

© MINISTRY OF EDUCATION, FSFE 2009 : PHYSICS. rope rope

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SECTION B (continued)

QUESTION 8

A potential difference of 12 V is found to produce a current of 0.50 A in a 3.6 m length of wire with a uniform radius of 0.40 cm. Calculate :

(a) the resistance of the wire. (1 mark)

(b) the resistivity of the wire. (2 marks)

QUESTION 9

A 24 V battery is connected in series with a resistor and an inductor where R = 10 and L = 5.0 H.

(a) Calculate the energy stored in the inductor when the current reaches its

maximum value. (1½ marks)

(b) Calculate the energy stored in the inductor at one time constant after the

switch is closed. (1½ marks)

QUESTION 10

A charged positive ion of charge 1.6 x 10-19 C has a mass of 2.50 x 10-26 kg. After being accelerated through a potential difference of 240 V, the ion enters a magnetic field of 0.500 T, in a direction perpendicular to the field. Calculate the radius of the ion’s path

in the field. (3 marks)

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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) An object at the end of a 5.0 m length of string is rotating in a horizontal circle as shown below.

The object completes 10 revolutions in 20 s.

(i) Calculate the period of the object’s rotation. (1 mark)

(ii) What is the linear speed of the object ? (2 marks)

(iii) Determine the angular velocity of the object. (1 mark)

(iv) Is the tension in the string greater or less than the weight of the object ?

Briefly explain your answer. (1 mark)

(b) On a planet in a galaxy, a 32 kg object weighs 60 N.

(i) What is the acceleration due to gravity on the planet ? (1 mark) (ii) If the planet’s radius is 9 600 m, what is its mass ? (2 marks)

(c) A baseball leaves the bat with a speed of 44 ms-1 at 30º above the horizontal. A 5.0 m high fence is located at a horizontal distance of 132 m from the batter. If the ball leaves the bat 1.0 m above the ground level, by how much does the ball

pass over the fence ? (2 marks)

Turn Over

© MINISTRY OF EDUCATION, FSFE 2009 : PHYSICS. 5.0 m

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SECTION C (continued)

QUESTION 2

(a) The graph below shows the forces acting on two objects X and Y of masses 2.0 kg and 1.0 kg respectively. The objects collide and the momentum of Y is shown after the collision.

Use the information given above to answer the following questions.

(i) What is the momentum of X before the collision ? (1 mark)

(ii) Calculate the momentum of X after the collision. (2 marks)

(iii) What is the speed of Y before the collision ? (1 mark)

(iv) Show that the collision is inelastic. (1 mark)

(b) A 1 500 N car on a hydraulic lift rests on a cylinder of radius 0.2 m. A connecting smaller cylinder of radius 0.04 m is driven by compressed air.

(i) What is the cross-sectional area of the smaller cylinder ? (1 mark) (ii) Determine the force applied on the smaller cylinder if it is to lift the car. (2 marks)

(c) A student on a rotating stool with arms outstretched, holds two objects making the total moment of inertia of the system 2.25 kgm2. While rotating at 5 rads-1, the student pulls the object inward so that the new moment of inertia is 1.8 kgm2.

What is the new angular speed ? (2 marks)

© MINISTRY OF EDUCATION, FSFE 2009 : PHYSICS. 2

2 -2

4

-4 6

6

-6 8

8

-8

10 12 14 16 18

Time (s) Force (N)

Y

X (before collision)

(after collision)

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QUESTION 3

(a) A solid cylinder of mass 3 kg and of radius 40 cm is connected to a 2 kg bucket by a light rope that is wound around the cylinder, which is free to rotate around the axle. [For cylinder, I = ½ MR2]

The cylinder starts to rotate from rest under the weight of the bucket which falls

for 3 seconds. How far does the bucket fall during this time ? (5 marks)

(b) The ear can be thought of as a pipe closed at one end and which resonates at a fundamental frequency of 3 kHz. Given that the body temperature is 37º C and the speed of sound is given by

273 T 331

v , how long is the ear drum ?

(Note that T is a Kelvin temperature.) (3 marks)

(c) Monochromatic light of wavelength 632.8 nm is incident normally on a diffraction grating containing 6 000 lines/cm. What is the diffraction angle at

which the second order maximum is observed ? (2 marks)

QUESTION 4

(a) A polythene ball of mass 2.0 g is suspended in an electric field of uniform strength 1 000 NC-1 in the horizontal direction towards the east.

The string makes an angle of 15º with the vertical. If the ball is in equilibrium,

calculate the net charge on the ball. (3 marks)

Turn Over

cylinder

rope

bucket

15º

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(b) A proton is released from rest in an electric field of magnitude 8 x 104 Vm-1, directed horizontally to the right.

The proton undergoes a displacement of 0.5 m in the direction of the field from X to Y.

(i) What is the change in the electric potential of the proton ? (1 mark) (ii) What is the increase in the electric potential energy of the proton ? (1 mark) The plates A and B are each 4 cm x 3 cm, and are now separated by a distance

of 2 mm. The connecting battery to this effective capacitor maintains a potential difference of 10 V, and is connected in a circuit as shown below.

(iii) Calculate the capacitance of this capacitor. (1 mark)

(iv) What is the maximum energy that the capacitor can store ? (1 mark) (v) Briefly explain what happens when the switch S is opened. (1 mark)

(c) A copper wire having a cross-sectional area of 8.16 x 10-7 m2, carries a constant current of 2 A. The density of free electrons is 8.5 x 1028 electrons per cubic metre. What are the magnitudes of the :

(i) current density ? (1 mark)

(ii) drift velocity of electrons in the conductor ? (1 mark)

C 10 V

L

flashing lamp S

proton

X Y

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QUESTION 5

(a) Manoa wants to convert a galvanometer to an ammeter which reads a full scale deflection of 2 A. The galvanometer has a coil resistance of 60 and gives full scale deflection with a current of 10 mA.

(i) Draw a diagram showing how Manoa should connect a shunt in order to

convert the galvanometer. (1 mark)

(ii) Calculate the value of the shunt used. (2 marks)

(b) A battery having an emf of 9.0 V delivers 120 mA when connected to a 70 load. Determine the internal resistance of the battery.

(2 marks)

(c) A 12 V cell is connected in parallel with a 8 V cell. A 6 and a 2

resistor are connected in series with the 8 V cell. A 4 resistor is connected in series with the 12 V cell.

(i) Use Kirchoff’s junction rule to write the relationship

between I1, I2 and I3. (1 mark)

(ii) Write the equations for the potential drops around loops

abefa and bcdeb. (2 marks)

(iii) Use the equations above to determine the values for I1, I2 and I3. (2 marks)

Turn Over

70

c d

12 V

8 V

6 I1

I2

I3

2 4

b

a f

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QUESTION 6

(a) A 20 cm length of conductor that is free to move is held in place between two thin conductors. When a 5 A current is directed as shown in the figure below, the wire segment moves upward without friction at a constant velocity.

If the mass of the wire is 15 g, calculate :

(i) the magnitude of the magnetic field (B). (2 marks)

(ii) the direction of the magnetic field required to move the conductor. (1 mark)

(b) In a model AC Generator, a 500 turn rectangular coil, 8.0 cm x 20.0 cm, rotates at 130 revs per minute in a uniform magnetic field of 0.50 T. Determine :

(i) the maximum emf induced in the coil. (2 marks)

(ii) the instantaneous value of the emf in the coil at t =

30 s, assuming

the emf is zero at t = 0 s. (1 mark)

(iii) the smallest value of t for which the emf is a maximum. (1 mark)

(c) A solenoid of radius 3.0 cm has 440 turns and length 22 cm.

(i) Find the inductance of the solenoid.

l

A N

L ₀ 2 (1 mark)

(ii) Calculate the rate at which the current must change to produce an

induced emf of 80 mV. (2 marks)

5.0 A

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QUESTION 7

(a) A resistor (R = 1 110 ), a capacitor (C = 0.25 F) and an inductor (L = 2.6 H) are connected in series across a 240 Hz AC source for which Vmax = 140 V. Calculate :

(i) the impedance of the circuit.

(ii) the maximum current delivered by the source.

(iii) the phase angle between the current and voltage. (3 marks)

(b) A transformer on a pole near a residential area steps down voltage from 3 400 V to 240 V. The transformer is to deliver 1 000 kW to a factory at 90% efficiency. Find :

(i) the power delivered to the primary.

(ii) the current in the secondary. (2 marks)

(c) A rod AB lies across two sets of rails which are joined by a wire CD. The wire has a resistance of 5 . The rails are 50 cm apart and the apparatus is in a magnetic field of strength 2 T.

Rod AB is moved to the left at a constant velocity of 8 m/s.

(i) Calculate the induced current and indicate the direction of current on

conductor AB. (2 marks)

(ii) Find the force which must be applied to conductor AB to keep it moving

at this constant velocity. (1 mark)

(iii) Find the rate at which heat is developed in the wire CD. (2 marks)

THE END

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COPYRIGHT : MINISTRY OF EDUCATION, REPUBLIC OF THE FIJI ISLANDS, 2009. x x x x x x

8 m/s

A

D

C B