97-11-AL - The Chinese University of Hong Kong · Web viewA block slides from rest down an inclined plane. The frictional force between the block and the plane is constant. Which

THE INCREDIBLE COLLEGE

PHYSICS A-LEVEL PAPER II

Time allowed : 3 hours

This paper must be answered in English.

SECTION A - Multiple-choice Questions - Answer ALL Questions

SECTION B - Answer Any THREE Questions

INSTRUCTIONS FOR SECTION A

1. All the answers should be marked on the Answer Sheet.

2. Note that you may only mark ONE answer to each question. Two or more answers will score NO MARKS.

3. All questions carry equal marks. No marks will be deducted for wrong answers.

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Useful Formulae in Advanced Level Physics

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SECTION A

There are 45 questions in this section. Answer ALL questions. Each question is followed by five suggested answers. Select the best answer in each case. You should spend 1 hour and 45 minutes on this section. Where necessary, take g to be 10 m s2 and take c to be 3 108 m s1.

1. The graph below shows the time variation of a net force, F, acting on an object of mass 2 kg. The object is initially at rest and then moves along a straight line. Which of the following statements is/are correct ?

(1) The object is accelerating in the first 4 seconds.

(2) The final momentum of the object is greater than 10 kg m s-1

(3) The maximum speed of the object is greater than 5 m s-1.

A. (1) onlyB. (3) onlyC. (1) and (2) onlyD. (2) and (3) onlyE. (1), (2) and (3)

2. A block slides from rest down an inclined plane. The frictional force between the block and the plane is constant. Which one of the following graphs best shows the variation of E, the sum of kinetic and potential energy of the block, with the distance travelled, s?

2. (Continued)

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s

EA.

s

s

ED.

EE.

s

EB.

s

EC.

F/N

t/s

5

4

3. Two identical balls, A and B, each suspended by a light inextensible string of length l to a common point X. A is raised and then released through an angle of 60o as shown. The collision between A and B is perfectly elastic. What are the speed of A and the speed of B, just after the collision?

Speed of A Speed of B

A. 0

B. 0

C.

D. 0

E.

4. A ball B is aimed to shoot at the target held by an electromagnet by adjusting the angle between the barrel of the toy gun and the horizontal as shown. The target will be released at the same time when B leaves the barrel of the toy gun.

Which of the following factors determine(s) the value of ?

4. (Continued)(1) The speed of the ball B on leaving

the toy gun.(2) The vertical height of the target

above the ball.(3) The horizontal distance of the ball

from the target.


5. The figure shows the vertical transverse cross-section of a frictionless circular track which banks at angle with the horizontal. The radius of the track is r. When a car is moving along the track, which of the followings about the car is/are correct?

(1) There is only one speed v that the car can drive without skidding.

(2) If the car is moving at a speed higher than v , the car will skid up the slope.

(3) If the car carries more passengers, it can move at a speed higher than v without skidding.


6. A stationary uranium nucleus of mass 238 units disintegrates by emitting an

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B

ll

60o

X

A

alpha-article. The mass of the resulting nucleus has a mass of 234 units. What percentage of the total kinetic energy generated in the decay of uranium-238 will be carried away by the alpha-particle?A. 1 %B. 13 %C. 47 %D. 82 %E. 98 %

7. An object connected to a spring vibrates horizontally on a smooth surface with a period of 2.0 s. It is set into simple harmonic motion by releasing it from maximum displacement A, measured from the right to the centre of motion. After what time will the object be at a displacement A/4 measured to left from the centre of motion?

A. 0.08 sB. 0.13 sC. 0.42 sD. 0.58 sE. 0.66 s

8. When a body performs simple harmonic motion, which of the following is/are /2 radian out of phase with the displacement?(1) impulse(2) velocity(3) acceleration


9. Four masses are attached to a light circular hoop of radius 1 m as shown in the following diagram. The resulting configuration is free to rotate about the x, y and z axes.

9. (Continued)Its moment of inertia about the x, y and z axes are Ix, Iy and Iz respectively.

(Given : m1 = 1 kg, m2 = 2 kg and m3 = 3 kg)

Arrange Ix, Iy and Iz in ascending order.

A. Ix < Iy < Iz

B. Ix < Iz < Iy

C. Iy < Ix < Iz

D. Iy < Iz < Ix

E. Iz < Ix < Iy

10. Two isolated point charges +Q and q, separated by r in vacuum, attract each other with a force F. If they are moved apart a further distance r, then the new force between them and the work done required are respectively

Force Work done

A.

B.

C.

D.

E.

11. Equal currents flow through two uniform copper wires; one of which has a diameter half of the other. The ratio of the drift velocity of electrons in the thin wire to that in the thick wire is

11. (Continued)A. 4 : 1B. 2 : 1C. 1 : 1

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m3

m2 m1

m3

x

y

z

D. 1 : 2E. 1 : 4

12. A source of e.m.f and internal resistance r is connected to an external resistor of resistance R. When R = r,(1) the total power supplied by the

source is maximum.(2) the source is operating at its

maximum efficiency.(3) the source is delivering the

maximum power to the external resistor.


13. A parallel-plate capacitor of capacitance C is formed by two rectangular metal plates having separation d. Now each of the plates is cut into two smaller identical ones to form two capacitors,

each with plate separation d2

. What is

the capacitance when they are connected in series?

A.18

C

B. 14

C

C. 12

C

D. CE. 2C

14. An uncharged capacitor C of capacitance 1000 pF is connected in parallel with a charged capacitor C1 of capacitance 250 pF which is initially charged to a p.d. of 2 V. The final p.d. across the capacitors is

14. (Continued)A. 0.2 VB. 0.4 VC. 0.6 VD. 0.8 V

E. 1.0 V

15. Two parallel straight conductors, separated by a distance r, carry the same current in the opposite direction. Which of the following statements is/are correct?(1) The two wires repel each other.(2) The force acting on each wire is

inversely proportional to r.(3) The wires produce a magnetic field

with minimum flux density midway between them.


16. Which of the following statements about the use of a Hall probe in measuring the magnetic flux density of a magnetic field is/are true?(1) The plane of the semiconducting

slice inside a Hall probe should be in parallel with the magnetic field.

(2) A Hall probe can only be used for measuring the magnetic flux density of a steady magnetic field.

(3) A Hall probe can be used for comparing the directions of two magnetic fields.


17. The coil of galvanometer is suspended at the end of a fibre and is wound on a light former. Which of the following factors will increase current sensitivity of the galvanometer?

17. (Continued)

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(1) Replace the fibre with a weaker one which has a smaller torsional constant.

(2) Increase the number of turns of the coil.

(3) Use a stronger magnet.


18. A solenoid is connected to an a.c. supply. A search coil is placed at the centre of the solenoid, with their axes parallel to one another. If the frequency of the a.c. supply is doubled and the amplitude of the current is halved, which of the following statements is/are true?

(1) The magnetic flux density inside the solenoid is halved.

(2) The maximum rate of change of magnetic flux through the search coil is unchanged.

(3) The frequency of the induced e.m.f. in the search coil is doubled.


19. A coil of inductance 4.0 H is connected in series with a switch S and a cell of

e.m.f. 12 V. The total resistance of the circuit is 3.0 . What are the initial rate of growth of the current when the switch is closed and the final steady value of current in the circuit?

Initial rate of Final steadygrowth value

A. 0 A 3 AB. 0 A 4 AC. 3 A 3 AD. 3 A 4 AE. 4 A 3 A

20. A d.c. motor is connected to a battery of 15 V. If the efficiency of the motor is 80 % at steady state, what is the back e.m.f.?

A. 3 VB. 6 VC. 9 VD. 12 VE. 15 V

21. Which of the following devices make(s) use of eddy currents?(1) Induction furnace(2) Electromagnetic damping in

galvanometers(3) Motor car speedometer


22. A 120 Vrms, 40 W bulb is connected in series with a capacitor and a 220 Vrms, 50 Hz mains. If the bulb is in its normal operation, the capacitance of the

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capacitor is

A. 1.06 FB. 4.82 FC. 5.75 FD. 8.84 FE. 9.63 F

23. The circuit shows a npn transistor and two resistors connected to a 6 V d.c. power supply. The current gain of the transistor is 150. At this setting, the base-emitter voltage is , the collector-emitter voltage and the collector current is . What must be the values of the load resistor RL and the base resistor RB?

RL RB

A. 2 k 265 kB. 2 k 300 kC. 1 k 265 kD. 1 k 300 kE. 1 k 325 k

24. In the circuit below, the LED is ON. Which of the following changes could turn it OFF?

24. (Continued)

(1) Decreasing the temperature.(2) Increasing R.(3) Moving the pointer P upwards.


25. What kind(s) of mechanical waves can be transmitted through gases and solids?

Gaseous medium Solid mediumA. longitudinal

wave onlylongitudinal wave only

B. longitudinal wave only

longitudinal and transverse waves

C. transverse wave only

transverse wave only

D. transverse wave only


E. longitudinal and transverse waves


26. A plane progressive wave is represented by the equation

y = 10 sin (500t 20x)where y is the displacement in millimetres, t is in seconds and x is the distance in metres measured from a fixed origin. The speed of the wave is

26. (Continued)A. 10 ms1

B. 20 ms1

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P

C. 25 ms1

D. 500 ms1

E. 104 ms1

27. An unpolarized light is incident at an angle other than the Brewster angle as shown below. An observer uses a polaroid to analyse the reflected light. When he rotates the polaroid slowly, which of the following about the light intensity is/are correct?

(1) The light intensity is constant.(2) The light intensity is zero at certain

moment.(3) The light intensity varies between

maximum and minimum values.


28. S1 and S2 are two sound sources and P is a point such that D >> a. At point P the displacements of the waves from S1 and S2 are denoted by y1(t), and y2(t), the amplitudes by A1 and A2 and the intensities by I1 and I2. Also let y(t), A and I denote the corresponding quantities of the resultant wave at P.

Which of the following statements is/are in general true?

28. (Continued)(1) y(t) = y1(t) + y2(t)(2) A = A1 + A2

(3) I = I1 + I2


29. A monochromatic light is incident normally on a grating and the first order image is observed at = 10. What is the highest order of image that can be observed?A. 2 B. 3 C. 4 D. 5 E. 6

30. The electromagnetic spectrum can be classified as different types of radiation. Which of the following statements correctly describe(s) the radiations?(1) Each radiation has well defined cut-

off frequencies or wavelengths distinguishing it from other radiations.

(2) The distinction of one radiation from another is determined by how the radiation is detected.

(3) The distinction of one radiation from another is determined by how the radiation is produced.


31. When a sound wave passes through air, an oscillatory motion is added to the normal random motion of the air molecules.

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31. (Continued)Which of the following diagrams best represents the actual oscillatory motion of the air molecules, in both magnitude and direction, at different points in a closed air column vibrating in its fundamental mode?

32. A truck carrying an observer and a sound source is moving with velocity of 30 ms1 towards a stationary reflecting surface. The apparent frequency received by the observer is f. If the truck is moving away from the surface at 30 ms1, the apparent frequency is f. Assuming the velocity of sound to be 330 ms1, find the ratio f/f.A. 1B. 1.2C. 1.44D. 2.4E. 2.88

33. Let be the intensity level at a point which is at a distance r from a sound source of power P. Assuming that the source emits sound uniformly in all directions, how will vary with log10r?

33. (Continued)

34. The angular magnification of an astronomical telescope is 10 when in normal adjustment. A beam of light parallel to the axis of the telescope is incident on the objective which has a diameter of 100 mm. If all the light entering the objective is collected by the eyepiece, what is the minimum diameter of the eyepiece?

A. 2 mmB. 5 mmC. 10 mmD. 20 mmE. 100 mm

35.

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35. (Continued)A liquid is flowing in a pipe as shown above. The cross-sectional areas at ‘a’ and at ‘b’ are A and 3A respectively and the velocities at 'a' is 4 ms1. If the pressure at ‘a’ and ‘b’ are equal, calculate the difference in levels h.

A. 0.35B. 0.53C. 0.71D. 0.80E. 1.06

36. An ideal gas is taken through the series of changes shown.

A. DA represents an isobaric expansionB. The work done by the gas during the

change AB is equal to that done on the gas during the change CD

C. No work is done on the gas during the change DA.

D. No work is done on the gas during the change CD.

E. No net work is done by the gas in completing one cycle.

37. An ideal gas is heated at constant pressure. Which of the following graphs best represents the variation of the internal energy per unit volume of the gas with temperature ?

37. (Continued)

38. A steel bar has a radius of r1 for half of

its length and a radius of r2 = r1 for the

other half. When subject to axial loading, what is the ratio of the extension l1 : l2 of the two halves?A. 1:2B. 1:4C. 4:1D. 2:1E. :1

39. The graph below shows the variation of the interatomic force F with the interatomic distance r. When F = F, what is the strain?

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39. (Continued)

A. r0rB. r / r0

C. (r r0) / r0

D. (r r0) / rE. (r0 / r)2

40. The voltage variation of two supplies Vx

and Vy with time are shown below. They are applied to the x-plates and y-plates of a CRO respectively.

Which of the following best represents the trace on the screen?

40. (Continued)

41.

The diagram shows five electron energy levels of a hydrogen atom. Which of the following statements is/are correct?(1) The atom is most stable when the

electron has zero energy.(2) When the electron is in the 13.6 eV

level, the atom can absorb 10.2 eV from a colliding electron.

(3) When the electron is in the 1.5 eV level, the atom can emit a photon of energy 1.9 eV.

41. (Continued)A. (1) only

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B. (3) onlyC. (1) and (2) onlyD. (2) and (3) onlyE. (1), (2) and (3)

42. In the investigation of the structure of the atom of a particular element, a scientist suggests the existence of four energy levels as shown below. E1 is the lowest energy, E4 is the highest. He proposes five possible energy transitions as shown below by the arrows.

Which one of the spectra below most closely corresponds to the suggested transitions?

43. Polonium 214 may decay into polonium 210 by emitting an particle followed by

A. a particle and a rayB. two particlesC. an particle and a particleD. two raysE. a ray

44. An isotope has a half-life of 8 years. After a period of 64 years, the fraction

of the isotope remaining is

A. 1/4B. 1/8C. 1/64D. 1/128E. 1/256

45. Which of the following phenomena of an atom can be explain by Rutterford’s model of an atom?(1) Most of the space outside the

nucleus of an atom is empty.(2) The characteristic spectrum of an

atom.(3) Electrons orbiting around the

nucleus of an atom do not radiate electromagnetic waves.


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END OF SECTION A

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SECTION B

Answer any THREE questions from this section. Write your answers in the ANSWER BOOK provided. You should spend 1 hour and 15 minutes on this section.

1. (a) State Newton's laws of motion. (3 marks)(b) State the principle of conservation of linear momentum and show that it can be

derived from Newton’s laws of motion. (3 marks)(c) An object placed on a turntable may curve outwards to the edge if the turntable

rotates at a high speed. A student says that there is a force acting on the object to push it outward. Comment on the student's argument with the aid of a diagram.

(3 marks)(d) Consider a solid cylinder of uniform density, mass M and radius r rolls down a rough

inclined plane without slipping as shown below. The moment of inertia of the solid cylinder about the axis through its centre of mass and perpendicular to the plane of

rotation is .

(i) A student says that the rolling of the solid cylinder is a combined motion of a pure translational motion and a pure rotational motion. Justify the statement. Write also equations to show the forces and torque acting on the solid cylinder. (Hint : Consider the torque by the frictional force on the solid cylinder about its centre of mass)

(ii) Hence derive an expression for the linear acceleration of the solid cylinder in terms of M, r, g and from (d)(i).

(iii) Determine whether a similar hollow cylinder of the same mass M and radius r will roll down the inclined plane at a greater or smaller acceleration. Explain briefly.

(7 marks)

2. A d.c. motor, as shown below, is designed in such a way that the field coil is connected to its armature in parallel. The motor runs at a steady angular velocity when a current I flows through the armature.

2. (Continued)

Some information about the motor are listed as follows: Number of turns of the coil in the armature is N. The area of the coil in the armature is A. The resistance of the coil in the armature is R. The magnetic field applied to the armature is B. The voltage supplied to the motor is V.

(a) Explain briefly the fundamental operation of this motor. (3 marks)(b) (i) Draw a diagram to show the position of the coil in the magnetic field at which

the coil is subjected to the maximum torque.(ii) Derive an expression for the maximum torque in terms of N, B, I and A from the

first principle. (4 marks)(c) What is the maximum induced e.m.f. in the coil? Express it in terms of , B, A and N.

(1 mark)(d) From the above results, give an account of what will happen in each of the following

situations.(i) A greater load is driven by the motor.(ii) The direction of the current flow in the circuit is reversed.(iii) A resistor is connected in series with the field coil.

(8 marks)

3. (a) (i) (1) Explain the difference between plane polarized light and unpolarized light. Give one example of each of them.

(2) Describe how one can use a piece of polaroid to test whether a beam of light is plane polarized or not.

(ii) When a beam of unpolarized light is incident onto a piece of glass or a thin layer of water, the reflected light is usually described as partially polarized.(1) What is the meaning of the term partially polarized ?(2) With the aid of an appropriate diagram, deduce an expression for the angle

of incidence at which the reflected light becomes plane polarized. Show your steps clearly. (9 marks)

3. (Continued)

(b) (i) (1) Explain the meaning of the term red shift.(2) Explain why red shift provides an evidence for the expanding universe.

(ii) Since the sun rotates about an axis passing through its centre, the wavelengths of light waves emitted from it differ at both ends of the diameter. Use Doppler effect to explain, quantitatively, how the rotational speed of the sun can be found by the above observations.

(7 marks)

4. (a) Suppose that there are N molecules of an ideal gas, each of mass m, inside a spherical container of radius r. The diagram below shows the path of one of the gas molecules travelling with speed c1 and rebounding elastically from the container wall at points P, Q and R.

(i) By considering there are N1 molecules with speed c1, N2 molecules with speed c2, etc and using the above model, show that the total pressure P exerted by the gas on the container wall is given by the expression

where V is the volume of the container and is the mean square speed of the gas. State your assumptions.

(ii) Hence, express the average kinetic energy of each gas molecule in terms of the absolute temperature T.

(8 marks)(b) The ideal gas equation is usually modified by the Van der Waals' equation

for a real gas. Account for the terms

where a and b are constants. (5 marks)

4. (Continued)(c) The graph below relates the pressure and volume of a fixed mass of an ideal gas that

is compressed isothermally from A to B.

Using the first law of thermodynamics, state and explain whether there is heat transfer to or from the gas and work is done on or by the gas. (3 marks)

5. (a) Draw the experimental set-up for investigating the collisions of moving electrons with gaseous mercury atoms. Discuss the importance of the results. (4 marks)

(b) (i) With the aid of diagrams, briefly describe and explain the characteristics of the hydrogen spectrum and the X-ray spectrum. Why do the lines in the X-ray spectrum have much shorter wavelengths?

(ii) Explain why dark lines are observed in the Sun’s spectrum.(9 marks)

(c) (i) What is meant by the word LASER ?(ii) List TWO properties that make LASER a suitable source for study of interference

and diffraction phenomena.(iii) Suggest TWO practical applications of LASER in daily life.

(3 marks)

END OF SECTION B

END OF PAPER

A

B

Volume

Pressure

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97-11-AL - The Chinese University of Hong Kong · Web viewA block slides from rest down an inclined plane. The frictional force between the block and the plane is constant. Which