PHY 111 / Page 1 of 1

INTI COLLEGE MALAYSIA

A-LEVEL PROGRAMME (CALUK)

PHY 111 : PHYSICS I SEMESTER EXAMINATION : APRIL 2003 SESSION

Section A There are 40 questions on this paper. Answer ALL questions. (40 marks) For each question there are five possible answers A, B, C, D and E. Choose the one you consider correct and record your choice in pencil on the Multiple Choice Answer Sheet provided. 1. The gravitational constant G has the SI unit A ms-2

B N m-2 kg-2

C m3kg-1 S-2 D m2 kg-2 E J m kg-1

2. The diagram show the scale readings of a travelling microscope focused in turn on each

of the ends of a short metal rod.

5 6 8 9 cm cm

0 5 10 0 5 10 On reading the vernier, an error of one division either way may be made. What is length of the rod and the associated error in the measurement? A 2.66 ± 0.01 cm B 2.68 ± 0.01cm C 2.68 ± 0.02 cm D 2.70 ± 0.01 cm E 2.70 ± 0.02 cm

3. Which of the following quantities has a unit that can be expressed in terms of just two

different SI base units? A area B charge C current D force E resistance

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4. The diameter of a steel ball is measured using a micrometer screw gauge. A student takes

an initial zero reading and then a reading of the diameter. The diagrams show enlargements of the screw gauge readings.

5 0 45

10 5 0

mm 0 mm 0

What is the diameter of the ball? A 3.48 mm B 2.04 mm C 1.98 mm D 1.92 mm E 1.42 mm

5. In term of the kilogram (kg), metre (m), second (s), and kelvin (K), what are the base

units of specific heat capacity? A ms-2K-1

B ms-1K-1 C m2s-2K-1 D m2s-1K-1

E kg-1m2K-1

6. The base units of the SI system include those of mass, kg ; length, m ; time, s ; electric current, A.

Which base units would be needed to express the SI unit of potential difference (the volt)? A kg and A only B m and A only C s and A only D m, s, and A E kg, m, s, and A

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7. A rod of length 1 metre has non-uniform composition, so that the centre of gravity is not at its geometrical centre. The rod is laid on supportsacross two top-pan balances as shown in the diagram. The balances (previously set at zero) give readings of 360g and 240g. 1 metre

240 360

Where is the centre of gravity of the rod relative to its geometrical centre?

A 101 metre to the left

B 101 metre to the right

C 61 metre to the left

D 51 metre to the right

E 51 metre to the left

8. A ruler of length 0.30 m is pivoted at its centre. Equal and opposite forces of magnitude

2.0 N are applied to the ends of the ruler, creating a couple as shown.

50

2.0N 50°

ruler

.

°

2.0N

pivot

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What is the magnitude of the torque of the couple on the ruler when it is in the position shown?

A 0.23 Nm B 0.39 Nm C 0.46 Nm D 0.60 Nm E 0.80 Nm

9. The diagram shows the jib of a tower crane . only three forces act on the jib: the tension T

provided by the supporting cable: the weight W of the jib: and a force P (not shown ) acting at point X.

W

T

X jib

The jib in equilibrium.

Which triangle of forces is correct?

T P W

T P

W

P T W

P T W

C D

A B

P

E.

W T

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10. A uniform plank of weight 60 N is 2000 mm long and rests on a support that i 600 mm from end E. At what distance from E must a 160 N weight be placed in order to balance the plank?

E 600mm

2000mm

A 150 mm B 225 mm C 375 mm D 450 mm E 200 mm

11. A car is travelling with uniform acceleration along a straight road. The road has marker

posts every 100 m. When the car passes one post, it has a speed of 10 ms-1 and, when it passes the next one, its speed is 20 ms-1. What is the car’s acceleration? A 0.67 ms-2 B 1.5 ms-2 C 2.5 ms-2 D 6.0 ms-2 E 7.0 ms-2

12. A light rod is acted upon by three forces P, Q and R. Which diagram could show the position and direction of each of the forces when the rod is in equilibrium?

P Q R

A E

P

P

Q

R

P B

Q

R

D Q

R

Q C

P R

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13. When a force of 4 N acts on a mass of 2 kg for a time of 2 s, what is the rate of change of

momentum? A 1 kg m s-2 B 2 kg m s-2 C 4 kg m s-2 D 8 kg m s-2 E 16 kg m s-2

14. The diagram shows the path of a projectile fired with a horizontal velocity v from the top

of a cliff of height h.

θ

v

h

Which of the following values for v and h will give the greatest value of the angle θ? v/ms-1 h/m A 10 30 B 10 50 C 30 30 D 30 50 E 50 10

15. A body starts from rest at time t= 0 and moves with constant acceleration. Which graph

best represent how s, the displacement of the body , varies with time?

t

s 0 0 t

0

0

D

0 t

E

0 t

s 0 0 t

s 0 0

s

A B C

s

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16. In the absence of air resistance, a stone is thrown from P and follows a parabolic path in which the highest point reached is T.

T

P The vertical component of acceleration of the stone is A zero at T. B greeatest at T. C greatest at P. D the same at P as at T. E lowest at T

17. A force of 10N acting on a certain spring gives an extension of 40mm. Two such springs

are connected end to end and this double length spring is extended by 40mm. Assuming that the springs conform to Hooke's law, what is the strain energy?

A 0.05J B 0.10J C 0.20J D 0.40J E 0.80J

18. A mass accelerates uniformly when the resultant force acting on it

A is zero. B is constant but not zero. C increases uniformly with respect to time. D is proportional to the displacement of the mass from a fixed point. E is same as the frictional force.

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19. A car of mass m has an engine which can deliver power P. What is the minimum time in which the car can be accelerated from rest to a speed v? A mv P B P mv C mv2 2P D 2P

mv2 E mv2 4P 20. An electric motor is required t haul a cage of mass 400 kg up a mine shaft through a

vertical height of 1200 m in 2.0 minutes. What will be the electrical power required if the overall efficiency is 80%? (Take g as 10 m s-2) A 3.2 kW B 5.0 kW C 32 kW D 50 kW E 3000 kW

21. What is the power required to give a body of mass m a forward acceleration a when it is

moving with velocity v up a frictionless track inclined at an angle θ to the horizontal? A mavg sin θ B mav sin θ + mgv C mav + mgv sin θ D ( mav + mgv ) sin θ E mav + mgv sin θ

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22. A constant force is applied to a body which is initially stationary but free to move in the direction of the force. Assuming that the effects of friction are neglible, which of the following graphs best represent the variation of P, the power supplied, with time t ?

A

0

P

23. The diagram

free-runninginclined at 3

What will bplane? ( g = A 20 JB 59 JC 64 JD 132 E 137

B C

D E

P 0

P 0

t

t

shows tw pulley, X 0° to the ho

2.0

4

30°

e the total k 9.8 ms-2 ) .

J J

o bodies X and starts from rest arizontal.

m

X .0kg

inetic energy of

t

P 0

t

P 0

t

Y connected by a light cord passing over a light, nd moves on a smooth plane

Y 5.0kg

the system when X has traveled 2.0m along the

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24. A crate is pushed 10m along a horizontal surface by a force of 80N. The frictional force opposing the motion is 60N. How much of the work done is converted into thermal energy and how much into kinetic energy of the crate? thermal energy/J kinetic energy/J A 200 600 B 200 800 C 600 200 D 600 800 E 600 1400

25. A raindrop of mass m is falling vertically through the air with a steady speed v. It

experiences a retarding force kv due t the air, where k is a constant. The acceleration of free fall is g. Which expression gives the kinetic energy of the raindrop? A mg k B mg2 2k2 C m3g2 k2 D m3g2 2k2 E m3g2k2 2

26. A small metal sphere of mass m is moving through a viscous liquid. When it reaches a

constant downward velocity v, which of the following describes the changes with time in the kinetic energy and gravitational potential energy of the sphere? kinetic energy gravitational potential energy A constant and equal to ½ mv2 decreases at rate of mgv B constant and equal to ½ mv2 decreases at rate of (mgv-½ mv2) C constant and equal to ½ mv2 decreases at rate of (½mv2-mgv ) D increases at rate of mgv decreases at rate of mgv E increases at rate of mgv decreases at rate of ( ½ mv2-mgv)

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27. On the ground the gravitational force on a satellite is W. What is the gravitational force on the satellite when at a height R/50, where R is the radius of the Earth? A 1.02W B 1.00W C 0.98W D 0.96W E 0.00W

28. Star X of mass 2M and star Y of mass perform circular motion about their common

centre of mass under their gravitational attraction.

What is the ratio Yon acting ForceXon acting Force , ignoring the effects of any other bodies?

A 4 B 2 C 1 D 2

1

E 41

29. In two widely-separated planetary systems whose suns have masses S1 and S2, planet P1

of mass M1 and planet P2 of mass M2 are observed to have circular orbits of equal radii. If P1 completes an orbit in half the time taken by P2 it may be deduced that A S1 = S2 and M1 =0.25 M2 B S1 = 4 S2 only C S1 = 4 S2 and M1 = M2 D S1 = 0.25 S2 only E S1 = 0.25 S2 and M1 = M2

30. A satellite of mass m is in a circular orbit of radius r about the Earth, mass M, and

remains at a vertical height h above the Earth’s surface. Taking the zero of the gravitational potential to be at an infinite distance from the Earth, what is the gravitational potential energy of the satellite? A mgh B -mgh C -GMm r D -GMm 2r E GMm 2r

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31. The Earth may be cosidered to be a uniform sphereof mass M and radius R. Which one of the following equation correctly relates the universal gravitational constant G to the acceleration of free fall g at the surface of the Earth? A G = gM R2 B G = R2 GM C G = gR2 M D G = M gR2 E G = gMR2

32. The gravitational potential energy Ep of a body varies with its distance r from the centre

of a planet as shown in the diagram below.

Ep

0 0 r

What does the gradient at any point on the curve represent? A the gravitational potential at that value of r B the gravitational field strength at that value of r C the force pulling the body towards the planet D the acceleration of the body towards the planet E the potential energy of the body at that value of r

33. Which one of the following is a property of uniform gravitational field? A It acts equally in all directions.

B Its field strength is the same at all point within it. C The gravitational potential has the same value at all points within it. D It produces zero force on stationary test mass placed in it. E Its direction is opposite to the direction of motion of a test mass released in it.

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34. A car of mass m moving at a constant speed v passes over a humpback bridge of radius of curvature r. Given that the car remains in contact with the road, what is the net force R exerted by the car on the road when it is at the top of the bridge? A R = mg + mv2/r B R = mg – mv2/r C R = mv2/r D R = mg E R = mv2/r-mg

35. Which of the following statements is correct for the particle moving in a horizontal circle

with constant angular velocity? A The linear momentum is constant but the kinetic energy varies. B The kinetic energy is constant but the linear momentum varies C Both kinetic energy and linear momentum are constant. D Neither the linear momentum nor the kinetic energy is constant. E The speed and the linear velocity are both constant.

36. A straight length of tape winds on to a roll rotating about a fixed axis with constant

angular velocity, the radius of the roll increasing at a steady rate.

v radius

Which one of the graphs below correctly shows how the speed v at which the tape moves towards the roll varies with time?

v v v 0 0 0 t 0 0 t 0 t A B C v v 0 0 D E

t 0 t 0

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37. The minute hand of a large clock is 3.0 m long. What is its mean angular speed? A 1.4 x 10-4 rad s-1

B 1.7 x 10-3 rad s-1 C 5.2 x 10-3 rad s-1 D 1.0 x 10-1 rad s-1 E 3.0 x 10-1 rad s-1

38. A mass of 0.050 kg is attached to one end of a piece of elastic of unstretched length 0.50

m. The force constant of the elastic (i.e. the force required to produce unit extension ) is 40 N m-1. The mass is rotated steadily on a smooth table in a horizontal circle of radius 0.70 m as shown below.

0.70m

What is the approximate speed of the mass? A 11 m s-1 B 15 m s-1 C 20 m s-1 D 24 m s-1 E 28 m s-1

39. A record on a turntable is rotating at a constant number of revolutions per second.

Which graph best represent the rotation between the speed v of a point on the record and its distance r from the centre of rotation?

v

v 0 0 r

A

v B

0 0 r

v

v C 0 0 r

0 0 r

D

E

0 0 r

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40. When the aircraft Concorde is moving in a horizontal plane at a constant speed of 650

ms-1, its turning circle has a radius of 80 km. What is the ratio of the centripetal force to the weight of the aircraft? A 8.3 x 10-4 B 0.54 C 1.9 D 52 E 540

SECTION B : Answer any FOUR (4) questions out of SEVEN (7) questions. (60 marks) Question 1 (a) What is meant by

(i) a systematic error, (2 marks) (ii) a random error? (2 marks)

(b) A student set up the circuit shown in Fig 1.1 in order to determine the resistance of wire

and hence the resistivity of the metal of the wire

A

The amme (i) St

Ho (ii) Ex

wi

V

wire

Fig 1.1

ter and voltmeter were both digital.

ate one possible random error which could occur in the use of the digital meters. w could this error be kept to a minimum? (2 marks)

plain why the voltmeter must have a resistance much greater than that of the re in order to avoid a systematic error in the use of the ammater. (3 marks)

PHY 111 / Page 16 of 16

(c) The following readings were obtained for the experiment in (b) Reading of the voltmeter = 1.30 ± 0.01V Reading of ammeter = 0.76 ± 0.01A Length of wire = 75.4 ± 0.2 cm Diameter of wire = 0.54 ± 0.0.2 mm Calculate, with its actual uncertainty, the value of

(i) the resistance of the wire, (2 marks) (ii) the resistivity of the metal of the wire, (2 marks)

expressing your results to an appropriate number of significant figures. (d) A second student repeated the experiment in (b) with the same length of wire. In this new

experiment, the supply voltage was varied and pairs of corresponding readings of the voltmeter and ammeter were tabulated. A graph showing the variation of current in the wire with p.d. across the wire was then plotted. Discuss the advantages of this procedure for the determination of resistance as compared with that used in (c).

(2 marks) Question 2

The graph, Fig 2.1. shows the speed of two cars A and B which are travelling in the same direction over a period of time of 40s. Car A, travelling at a constant speed of 40ms-1, overtakes car B at time t= 0. In order to catch up with car A, car B immediately accelerates uniformly for 20s to reach a constant speed of 50ms-1.

speed/ms-1

50 B 40 A 25 0 0 20 40 time/s

Fig. 2.1 (a) How far does car A travel during the first 20s? (2 marks) (b) Calculate the acceleration of car B in the first 20s. (2 marks) (c) How far does car B travel in this time? (3 marks)

PHY 111 / Page 17 of 17

(d) What additional time will it take for car B to catch up with car A? (3 marks) (e) How far will each car have then travelled since t = 0? (3 marks) (f) What is the maximum distance between the cars before car B catches up with car A?

(2 marks) Question 3 The following data concern a tennis ball at given instant just before it is struck by a tennis racket; horizontal momentum of the tennis ball = 2.4 Ns, kinetic energy of tennis ball = 45J (a) Why it correct to give the direction of the momentum but not of the kinetic energy? (2 marks) (b) Write down in terms of the mass m and the velocity v of a body, expressions for

(i) the momentum, (2 marks) (ii) the kinetic energy. (2 marks)

(c) Use your answer to (b) to help you to calculate the mass and the velocity of the tennis

ball. (4 marks) (d) When the racket hits the ball it strikes it with a constant force of 60N in a direction

opposite to its momentum, bringing it to rest momentarily. Calculate (i) the time the tennis ball takes a stop, (3 marks) (ii) the distance the tennis ball travels while stopping. (2 marks)

PHY 111 / Page 18 of 18

Question 4

The Normandy Bridge over the mouth of the Seine is constructed in the way shown in Fig 9.1.Two towers were sunk into the river bed and the roadway, which is supported by many cables, was made in stages. One of each cable is attached to the roadway. Each cable is therefore an inverted V. As you pass over the bridge there are cables on both your right hand side and your left hand side. Having many cables is a much better system than of a traditional suspension bridge which relies on the immense tensile strength of one pair of cables taking the entire load. Simplified data concerning the bridge are given below.

(a) (b)

(c)

tower cable

160m θ A

400m 800m 400m

Fig. 9.1

Length of bridge supported by the towers = 1600m Height of tower above roadway = 160m Total mass of all the cables = 1.4 x 106kg Mass of roadway = 8.5 x 106kg Maximum mass of load of traffic = 11.5 x 106kg (assume uniform distribution ) Horizontal distance between cables = 20m Vertical distance between cables = 8m Number of cables = 80

What reason does the paragraph give for the construction with many inverted V cables? (2 marks)

Calculate the maximum tatal mass which each of the two towers may need to support. Mass = kg (2 marks)

Calculate the mass of 20m of roadway and the traffic which those 20m of roadway may have to support. Mass = kg (2 marks)

PHY 111 / Page 19 of 19

(d) Calculate the angle , θ, between a cable and the horizontal.

Angle to horizontal = (3 marks) (e) Draw a force diagram for a fully laden 20m section of road at A. Explain how this road

section is in equilibrium. (4 marks) (f) Calculate the tension in a cable when the bridge is fully laden. (The tension in all cables

is assumed to be the same.) tension = N (2 marks)

Question 5 (a) An object accelerates uniformly in a straight line from velocity u to velocity v in time t,

as shown in Fig 1.1

v velocity u 0

0 time t Fig. 1.1

(i) Write down an expression for the acceleration a in terms of u, v and t.

(3 marks) (ii) Use Fig. 1.1 and your answer to (I) to show that s, the distance traveled, is given

by s = v2 – u2 (4 marks) 2a

PHY 111 / Page 20 of 20

(b) A cylinder of length 1.20m, area of cross-section 8.30 x 10-5m2, and mass 0.777kg falls from rest so that its base drops from a height of 2.30m above the ground, as shown in Fig. 1.2

1.20m 2.30m

Fig. 1.2 (i) Calculate, ignoring air resistance,

1. the speed of the cylinder just before it hits the ground, (4 marks) 2. the kinetic energy of the cylinder just before it hits the ground. (4 marks)

Question 6 (a) (i) State Newton’s law of gravitation. (1 mark)

(ii) The first definition of the metre was one ten-millionth of the distance between the north pole and wthe equator of the Earth. Use this information to estimate the radius of the Earth. State one assumption which you have made in your estimation. (1 mark)

(iii) Use your answers to (I) and (ii) to deduce the gravitational force acting on a 1.0kg

mass at the Earth’s surface. The Earth may be considered to be a sphere of mass 6.0 x 1024kg. (1 mark)

(b) (i) What gravitational force does the Earth exert on a 1.0kg mass which is at a

distance of 3.8 x 108m from the centre of the Earth? (2 marks)

(ii) Assuming that the Moon travels at a constant speed around the Earth in a circle of this radius (3.8 x 108 ), with the Earth at the centre of the circle, calculate the acceleration of the Moon. Show the direction of this acceleration on a sketch diagram. (2 marks)

(iii) Calculate the period of the Moon’s rotation. (2 marks)

PHY 111 / Page 21 of 21

(c) A satellite orbits the Earth in a circular path of radius r. The period of the orbit is T.

(i) Find the acceleration of the satellite. (3 marks) (ii) Hence show that

T2 = 4π2 r3 GM Where M is the mass of the Earth. (3 marks) Question 7 (a) Describe qualitatively how it is that a body which is travelling in a circle with uniform

speed has acceleration. Show on a diagram the direction of this acceleration in relation to the direction in which the body is travelling. (3 marks)

(b) State the equation for the force of attraction F between two point charges of equal

magnitude, +q and –q, when placed a distance r apart in a vacuum. (2 marks) (c) There is a sub-atomic particle of the same mass as the electron but with a positive charge

equal in magnitude to the charge of the electron. This particle is called a position. Calculate the force between an electron and a positron when they are separated by a distance of 1.30 x 10-10m. (2 marks)

(d) It is possible for an electron and a positron to move in a circular orbit as shown in Fig.

2.1. This system is called positronium and it is very unstable.

-1.60 x 10-19C

1.30 x 10-10m

Fig.2.1 Using your answer to part (c) calcul (i) the acceleration of the electr(ii) the radius of the orbit of the(iii) the speed of the electron in i(iv) the time taken for one revolu

Phy111(f)/Ms.Word/Apr’03/ML

+1.60 x 10-19C

ate

on (mass 9.11 x 10-31kg ), (2 marks) electron, (2 marks) ts orbit, (2 marks) tion of the electron. (2 marks)

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