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S.6 Final Exam PHY

This paper must be answered in English. 1 Write your Name, Class and Class number in the

spaces provided on the this cover. 2 This paper consists of THREE sections, Section A,

Section B and Section C. Section A carries 30 marks, Section B carries 16 marks and Section C carries 54 marks.

3 Answer ALL questions in each section. Write your

answers of Section A in the MC answer sheet and write your answers of Section B and Section C in the spaces provided in this Question-Answer Book.

4 The last page of this question paper contains a list

of physics formulae which you may find useful. 5 Unless otherwise specified, numerical answers

should be either exact or correct to 3 significant figures.

Question-Answer Book

Time: 3 hours

Date: 21 – 6 – 2011

Secondary Six (Advanced Level)

FINAL EXAMINATION PHYSICS

LIU PO SHAN MEMORIAL COLLEGE

(2010-11)

Name

Class

Class number

Teacher's Use Only

Question Marks

Section A

1 – 20

Section B

21

22

Section C

23

24

25

26

Total

LPSMC S6 Physics Final Exam (2010-11) p. 1

Section A: Multiple Choice Question (30 marks) (1) There are 20 M.C. Questions in this section. All questions carry equal marks. (2) Answer ALL questions. All the answers should be marked on the M.C. Answer Sheet

provided. No marks will be deducted for wrong answers. (3) Where necessary, take the acceleration due to gravity to be 10 m s-2.

1.

m

θ M

smooth

ground A wedge of mass M is fixed on the horizontal ground. A block of mass m slides down the

wedge’s smooth surface as shown. Which of the following statements is/are correct?

(1) The block accelerates down the wedge. (2) The normal reaction exerted on the wedge by the block is mg cos θ (3) The normal reaction exerted on the wedge by the ground is (M + m) g

A. (1) and (2) only B. (1) and (3) only C. (2) and (3) only D. (1), (2) and (3)

2.

R2

R4

R1

R6

X

Z

ground R5

Y

R3

Three metal cylinders X, Y and Z rest on a horizontal ground as shown. Each cylinder weighs

100 N. All the reaction forces acting on the spheres are indicated as R1 to R6. Which statement is INCORRECT ? (Assume that there are no frictions between the cylinders.)

A. R1 is greater than 50 N. B. R5 is less than 150 N. C. R2 and R4 form an action and reaction pair. D. There is friction between the ground and the cylinders Y.


3.

A uniform rectangular block PQRS, 0.5m × 1.2 m and of mass 10 kg, rests on the ground as

shown. A force is applied to rotate the block about an axis normal to the paper through P so that it then takes an upright position PQ′R′S′. During the process, which of the following statements is/are correct?

(1) The maximum gravitational potential energy of the block is 60 J. (2) The total change of gravitational potential energy of the block is 35 J (3) The moment of weight about P is a minimum when the block is at its upright position.

A. (1) only B. (2) only C. (1) and (3) only D. (2) and (3) only

4.

A bob of mass m is suspended by a string with tension T. The bob can either make to swing in a simple pendulum or to whirl in a horizontal circular path. Which of the following statements is are correct?

In both cases, (1) the bob moves with periodic motion. (2) the bob is accelerating.

(3) T cos θ = mg at the instant shown. A. (1) and (2) only B. (1) and (3) only C. (2) and (3) only D. (1), (2) and (3)

mg

T

θ

mg

T

θ

0.5 m

1.2 m R S

Q′ R′

ground

PQ S′


5. For a particle performing uniform circular motion about a fixed point, which of the following

physical quantities of the particle remain unchanged ?

(1) acceleration (2) angular velocity (3) kinetic energy

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only 6.

O P Q A light rigid rod is hinged smoothly at O at one end. Two small beads of the same mass are

fixed to the mid-point P and the other end Q of the rod respectively as shown. Initially the rod is held horizontal and it is then released from rest. What is the acceleration of the bead at Q when the rod reaches the position vertically below O ?

A. g

56

B. g57

C. g5

12

D. g5

17

7.

QP

A ball falls freely onto a light vertical spring firmly fixed to the ground. When the ball

reaches the spring at position P, it starts to compress the spring until reaching the lowest position Q as shown. Which statement is INCORRECT ? (Neglect air resistance.)

A. The speed v of the ball increases and then decreases from P to Q. B. The magnitude of the net force F acting on the ball increases and then decreases

from P to Q. C. The gravitational potential energy of the ball decreases from P to Q. D. The energy stored in the spring increases from P to Q.


8.

2 kg

3 kg k

A 2 kg block is placed on top of a 3 kg block which is connected to a wall by a light spring of

force constant k. The two blocks together perform simple harmonic motion with amplitude A on a smooth horizontal surface as shown. What is the magnitude of the frictional forces between the blocks when they are at maximum displacements from the equilibrium position ?

A. 0 B. kA

52

C. kA53

D. kA32

9. A simple pendulum oscillates with a period of 2 s at the Earth’s surface. When it is moved to

the surface of a certain planet, the period of oscillation becomes 5 s. Which statements are correct ?

(1) The length of the simple pendulum is about 1 m. (2) The period would be lengthened if a heavier pendulum bob is used. (3) The gravitational acceleration on the planet’s surface is greater than that on the Earth’s

surface.

A. (1) only B. (2) only C. (1) and (3) only D. (2) and (3) only

10.

X Y

Earth

Two identical satellites X and Y are moving in two circular orbits around the Earth as shown. Which statement is correct ?

A. The period of X is smaller than that of Y. B. The speed of X is smaller than that of Y. C. The gravitational force on X is greater than that on Y. D. The gravitational potential energy of X is smaller than that of Y.


11. The figure shows the equipotential lines at 10 V intervals drawn to scale. Which of the points

A, B, C and D has the greatest electric field strength ?

10 V 20 V 30 V × C


×

A

0 V

×

B D ×

12. Two metal spheres P and Q carrying positive charges are separated by a large distance.

Sphere P is smaller and the spheres are joined by a straight conducting wire.

P Q

Which statements are correct when a steady state is reached ?

(1) Spheres P and Q are at the same electric potential. (2) The quantity of charge on P is smaller than that on Q. (3) The surface charge density on P is smaller than that on Q.


13.

R2 P

R4

R3

Q

R1

G

Four resistors are connected to a cell as shown. The reading of the galvanometer G is zero.

Which statements are correct ?

(1) Points P and Q are at the same potential. (2) The potential difference across R1 and R3 is the same. (3) The current through R1 and R2 is the same.


14. A student requires a capacitor of 3 μF but the capacitors available are of capacitance 2 μF.

Which combinations of 2 μF capacitors would give the required capacitance ? (1) (2) (3)


15.

R

C

2C S

initially charged

initially uncharged

A charged capacitor of capacitance C is connected to another initially uncharged capacitor of

capacitance 2C through a switch S and a resistor R as shown. After the switch S is closed and a steady state is reached, which statement is INCORRECT ?

A. The potential difference across the capacitors is the same. B. The potential difference across the capacitor of capacitance C is reduced to

31 of its

original value. C. The total charge on the two capacitors remains unchanged. D. The total energy stored in the two capacitors remains unchanged.

16. X Y In the above figure, X and Y are two long straight parallel wires carrying equal currents in the

same direction. Wire X experiences a magnetic force of 0.1 N m−1. When a uniform magnetic field pointing into the paper is applied to both wires (NOT shown in figure), wire X will experience a resultant magnetic force of 0.5 N m−1. Find the resultant magnetic force experienced by wire Y. (Neglect the Earth’s magnetic field.)

A. 0.3 N m−1 to the left B. 0.3 N m−1 to the right C. 0.6 N m−1 to the left D. 0.6 N m−1 to the right

LPSMC S6 Physics Final Exam (2010-11) p.7

17. uniform electric field A proton and an α-particle of the same initial velocity enter a region of a certain width having

a uniform electric field as shown. The initial velocities of both particles are perpendicular to the field. Find the ratio of the kinetic energy gained by the proton to that gained by the α-particle when they just leave the field.

A. 1 : 1 B. 1 : 2 C. 2 : 1 D. cannot be determined as the electric field strength is unknown

18. Y S P

X

current-carrying wire

R Q The figure shows a rectangular coil PQRS moving to the right with constant speed. A long

straight wire XY carrying a steady current lies in the plane of the coil. Which of the following gives the correct direction of the induced current in the coil and the resultant magnetic force acting on the coil ?

direction of induced

current in the coil resultant magnetic force

acting on the coil A. anti-clockwise to left

B. anti-clockwise zero C. clockwise to left D. clockwise zero


19.

12 V, 0.4 Ω

S

A

M

In the above circuit, the cell has e.m.f. 12 V and internal resistance 0.4 Ω. When the switch S is open, the bulb is brightly lit and the ammeter A of negligible resistance reads 5 A. The motor M starts to rotate when S is closed. The ammeter reading finally increases to 10 A but the bulb becomes dimmer. What is the drop in the voltage across the bulb when S is closed ?

A. 6 V B. 5 V C. 4 V D. 2 V 20. When the switch is closed, which of the following statements is/are correct ? (1) The current will rise initially at the rate of 6 A s-1. (2) The final value of the current is 1.5 A. (3) The final energy stored in the inductor is 4.5 J. A. (1) only B. (2) only C. (1) and (2) only D. (2) and (3) only

End of Section A


Section B: Essay-type Question (16 marks)

(1) Answer ALL questions in this section. (2) Write your answers in the spaces provided.

21. (a) A bucket of water can be swung round in a vertical circle without spilling. Explain the

phenomenon with the aid of a diagram. (3 marks)

(b) A small mass m is supported by two identical light springs A and B inside a closed hollow smooth tube as shown in Figure 21.1. Each spring has a force constant k and with one end fixed on the inner surface of the tube. The springs produce equal and opposite compression forces on the mass. A rigid rod connects the tube to a fixed point O such that the tube’s centre is at a distance L from O.

Now the tube is made to rotate horizontally about O at a constant angular velocity ω, with the springs remain in the radial direction. The equilibrium position of the mass is seen to shift by a distance x. (Assume that the springs are always in compression state.)

(i) With the aid of a free-body diagram, account for this observation and explain the

direction of the shift. (ii) Derive, with explanation, an expression for the shift x in terms of ω, k, L and m.

Assume L >> x. (5 marks)

TOP VIEW O

L

k km

A BFigure 21.1


22. (a) A circuit consists of a battery and a resistor connected by conducting wires of negligible resistance.

(i) Distinguish between the electromotive force (e.m.f.) of the battery and the potential difference (p.d.) across its terminals.

(ii) Explain why the potential difference across the terminals of the battery is smaller than its e.m.f. (4 marks)

(b) You are asked to demonstrate the change in the terminal p.d. of a supply when delivering

a current. With the aid of a diagram, describe how you would carry out the experiment using a 12 V 24 W ray box lamp and some additional apparatus. Explain how the internal resistance of the supply could be estimated and state the source(s) of error.

(4 marks)


End of Section B


Section C: Structural Questions (54 marks) Instructions:

(1) Answer ALL questions in this section. (2) Write your answers in the spaces provided in this Question/Answer Book. In

calculations you are advised to show all the main steps in your working. (3) Where necessary, take the acceleration due to gravity to be 10 m s-2.

Question No. 23 24 25 26

Full Marks 13 15 13 13 23. Figure 23.1 shows a tennis ball of mass 0.06 kg struck horizontally by a racket at A at a height

of 1.25 m above the ground. The ball hits the ground at B and rebounds so that it just goes over an obstacle at C at the highest point of its path. During its impact with the ground, the vertical component of the ball’s velocity is reduced by 20%. (Assume that the ground is smooth and neglect air resistance.)

` A C

(a) Calculate the time of flight of the ball from A to B. Hence, find the horizontal and

vertical components of the ball’s velocity at B just before impact. (4 marks)

Figure 23.1 h

B 1.25 m

ground

3.5 m


(b) (i) Calculate the speed of the ball at B just after impact. (2 marks)

(ii) Find the magnitude of the average force exerted by the ground on the ball during

impact at B if the contact time of the ball and the ground is 0.04 s. (3 marks)

(c) Estimate the height h of the obstacle. (2 marks)

(d) If friction exists between the ball and the ground, decide whether the ball would take path

P or Q as shown in Figure 23.2. Explain your answer. (2 marks)

h B

C

ground

Figure 23.2 P

Q


24. A light conducting ball of radius a is suspended by a nylon thread well above the bench and far

away from other apparatus as shown in Figure 24.1. Given : permittivity of free space εo = 8.85 × 10−12 F m−1

50 MΩ + −

E.H.T. bench

Figure 24.1 (a) Indicate in Figure 24.1 how the ball should be connected to the E.H.T. so that it is charged

to −4 kV. (1 mark)

(b) (i) Sketch in the space provided the variation of electric potential V with distance r from the ball’s centre. (2 marks)

V

r 0

(ii) Derive an expression for the capacitance of the ball. (2 marks)


(iii) If the ball’s radius a is 5 cm, find the charge on the ball and the electrical potential

energy stored in it. (4 marks)

(c) The conducting ball is now placed midway between two parallel metal plates connected to

an E.H.T. via a galvanometer as shown in Figure 24.2.

galvanometer

+ – E.H.T.

metal plate

Figure 24.2

(i) State how to make the ball start shuttling continuously between the metal plates. Explain why it can shuttle between the plates. (3 marks)

(ii) State and explain how the average current registered by the galvanometer is affected if the separation of the plates for the shuttling ball is decreased. (3 marks)


25. (Given: permeability of free space = 4π x 10-7 H m-1) A large square metal coil ABCD of dimensions 0.06 m x 0.06 m and negligible resistance is

connected to a resistor of resistance 100 Ω. The coil is placed in the narrow gap between the two identical solenoids, PQ and RS, which are placed coaxially. The axis of the solenoids is perpendicular to the plane of the coil. Each solenoid is 36 cm long, has 1200 turns and a square cross-section of 0.03 m x 0.03 m.

Figure 25.1

The current in the solenoid I varies with time t as shown in Figure 25.2. The currents in the solenoids are flowing in the clockwise directions when they are viewed from the end P.

Figure 25.2

0 0.4 0.8 1.6 time t / s

current I / A

1.2

A

B

C

D

100 Ω

P Q R S


(a) Calculate the maximum magnetic flux density in the space between the solenoid. State

its direction. (3 marks)

(b) Calculate the maximum magnetic flux linking the coil. Hence calculate the induced current produced in the first 0.4 s. (3 marks)

(c) What is the direction of induced current obtained in (b)? Explain your answer with the help of Lenz’s law. (4 marks)

(d) Sketch the variation of induced current I’ in ABCD with time. The direction of induced

current along ABCD is taken as positive. (3 marks)

0 0.4 0.8 1.6 time t / s

induced current I’ / A


26. The graphs in Figure 26.1 show how the capacitive reactance XC of a capacitor C and inductive

reactance XL of a pure inductor L vary with frequency f respectively when each is connected to a sinusoidal a.c. supply.

-20

-10

0

10

20

30

40

10 20 30 40 50 60 70 80 90 f/Hz

X/Ω

XL

XC

Figure 26.1

(a) Using the graphs, estimate the capacitance of the capacitor and the inductance of the

inductor. (4 marks)


(b) A bulb of power rating “10 V 5 W” is connected to a sinusoidal a.c. power supply of r.m.s. output voltage fixed at 12.5 V but with variable frequency f. In order that the bulb will work at its rated power, two methods using the capacitor C and the inductor L respectively are suggested in the circuits below:

Circuit 1 Circuit 2

10 V 5 W

12.5 V, f1

C

~12.5 V, f2

L

~

10 V 5 W Figure 26.2 (a) Figure 26.2 (b) (i) What is the operating resistance of the bulb ? (1 mark)

(ii) Use the graphs in Figure 26.1, or otherwise, to find the frequencies and

respectively of the power supply in the two suggested methods. Show your working. (4 marks)

1f 2f


(iii) The bulb is now connected in series with the capacitor C and the inductor L as shown in Figure 26.3. If the frequency f of the power supply is varied, use the graphs in Figure 26.1 to estimate the frequency range such that the bulb is not exceeding its rated power. (4 marks)

12.5 V, f

L

10 V 5 W

~

C

Figure 26.3

End of Section C

End of Paper


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