AL Physics 1982-2004 Essay

82 AL Physics/Essay/P.1

HONG KONG ADVANCED LEVEL EXAMINATION AL PHYSICS 1982 Essay Type Question

1. (a) Describe how you would measure the thermal conductivity of a liquid, which is a poor conductor of heat, pointing out the precautions you would take to ensure an accurate result. (b) Explain (i)

the observed difference between the temperatures of the seawater and the air during the night-time in the autumn in Hong Kong, and

(ii)

the survival of fish in frozen-over ponds during the winter in North China.

2. Give accounts of the physics of the working of (a) a Geiger-Muller tube, and (b) a cloud chamber, in their use to detect ionizing radiations, contrasting the different techniques which would have to be used to distinguish between α, β and γ radiations.

3. Explain form first principles the following phenomena: (a) The colours observed when viewing an oil film on water, giving the reasons why the film must be thin, and (b) the absence of high frequencies to an observer standing outside and to the side of an open door leading into a room where music is being played. (Consider velocity of sound = 340 m/s.)


4. (a) Carefully distinguish between the characteristics of progressive and stationary transverse waves, drawing diagrams showing the displacements of the propagating medium particles at selected times during a complete period. (b) Draw diagrams showing the stationary wave patterns which are excited in (i)

a guitar string,

(ii)

an open-ended organ pipe and

(iii) a closed-end organ pipe, considering both (1) the fundamental and (2) the first overtone frequencies. Show how these frequencies are related to the appropriate physical dimension of each instrument.

5. Compare qualitatively and briefly explain the differences between the forms of the electromagnetic wave spectra emitted by (a) a hydrogen discharge tube, (b) the sun, and (c) an X-ray tube. (Note: Mathematical derivations are not expected.)


6. (a)

P S1 S2 m A small body of mass m is suspended form a fixed point P by two springs S1 and S2 as shown. The force constants of the springs are f1 and f2 respectively. If the body is pulled vertically downwards through a small displacement show that it subsequently moves with simple harmonic motion of period 1

 ( f + f2 )m  2 2π  1  . f f 1 2   Assume that the masses of the springs are negligible compared with m. (b) Consider a single spring (of force constant f) set into simple harmonic motion as in part (a). (i)

Sketch two cycles of the time variations of: (1) the position, (2) the velocity, and (3) the acceleration of the suspended body.

(ii)

Also sketch two cycles of the time variations of: (1) the kinetic energy, and (2) the potential energy of the system.

On your sketches indicate the maximum values attained in each case in terms of the force constant f, the maximum amplitude A and the period T of the oscillation.

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1. (a) Explain why the speed of travel of a gas odour (smell) across a room is very slow compared with the actual speeds of the gas molecules. (b) Briefly describe an experimental arrangement for measuring the rate of diffusion of bromine. (c) Given a knowledge of the r.m.s. molecular speed and the known rate of diffusion of bromine, show that it is possible to obtain estimates of (i)

the mean free path of the molecules (random walk statistical rule to be assumed), and

(ii)

the size of the molecules, taking into consideration a typical volume change from liquid to gas.

(d) Briefly explain how the separation of the accomplished.

235

U and

238

U isotopes of uranium may be

2. Describe briefly the methods adopted in the measurement of (a) a steady magnetic field using a Hall probe, and (b) an alternating magnetic field using a search coil. Compare the different physical mechanisms in these tow methods and derive any necessary mathematical expressions. Comment briefly on the main factors that might affect the accuracy of the measurements.


3. (a) Explain qualitatively, in terms of energy, what is meant by ‘force vibrations’ (oscillations) and ‘resonance’ in physical systems. (b) Give one example each of ‘resonance’ for the following types of system: (i)

mechanical,

(ii)

acoustical,

(iii) electrical, and (iv) atomic. For each of the examples you have chosen, explain clearly and concisely the factors affecting the resonant frequency and the sharpness of the frequency response. Mathematical derivations are not expected.

4. (a) By considering one practical example of each of the following phenomena: (i)

the refraction of light, and

(ii)

the interference of light,

show how these phenomena can be explained by assuming that light possesses a wavelike nature. (Note: No mathematical derivations are needed for (ii).) (b) Under certain experimental conditions, it is found necessary to assume that light possesses a particle-type, rather than a wave-like nature. Briefly describe such an experiment and explain how the results lead to this conclusion. (c) In some cases, wave-like properties have been observed for matter: such as in the diffraction of moving electrons. How may the wave and particle theories be reconciled in this particular case?


5. Describe the working principles of a moving coil type of (a) microphone, and (b) loudspeaker. For each example explain, with the aid of a diagram, the basic construction. You should indicate on your diagrams the directions of the corresponding sound vibrations and the flow of electric currents at a particular instant. Briefly suggest possible reasons for the reproduced sounds being different from the original sounds when such devices are used.

6. (a) A battery of e.m.f. E and negligible internal resistance is connected in series with a resistor of resistance R, a capacitor of capacitance C and an open switch. After the switch is closed, derive expressions for (i)

the total work done in charging up the capacitor, and

(ii)

the total energy dissipated in the resistor, using the expression for instantaneous Joule heating.

Discuss these results in relation to the total energy delivered by the battery. (b) The battery is now replaced by an a.c. source of voltage E = E0 sin ωt, ω being the angular frequency and t the time. With the switch closed, and making the assumption that ωCR << 1, determine expressions for the current I, and the power P delivered to the circuit at any instant. Sketch the time variations of E, I and P. Comment on the result for P.

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1. (a) (i)

Using a practical example, demonstrate what is meant by ‘the conservation of mechanical energy’.

(ii)

By means of a further practical example, show that in ‘real-life’ situations mechanical energy is often not conserved.

(b) Derive Bernoulli’s equation for fluid flow: P + hρg +

1 2 ρv = a constant. 2

(c) Explain why Bernoulli’s equation is not strictly applicable to (i)

a gas, and

(ii)

a viscous liquid flowing through a narrow tube.

(d) With the aid of diagrams and Bernoulli’s equation, explain the observed effects of (i)

the motion of a spinning ball, and

(ii)

the mixing of coal gas and air in a bunsen burner.

2. (a) Explain what is meant by a scale of temperature for a thermometer. (b) Considering the scales of two thermometers based on two different physical properties, explain why the observed temperatures might be found to differ. (c) Give brief descriptions (not including theory or calibrations) of two different types of thermometer which could be used to measure accurately, in the range 200 ºC - 300 ºC, (i)

a steady temperature, and

(ii)

a rapidly changing temperature.


3. (a) Compare the main physical characteristics of the light emitted by (i)

a gas discharge tube, and

(ii)

a gas laser.

(b) Explain in detail the light production mechanisms of these two sources. (c) Describe TWO different applications of lasers outside their use in physics laboratories, explaining why they are employed.

4. The concept of waves can be applied to (1) a musical sound, and (2) a V.H.F. radio transmission. For these two types of waves describe (a) their main propagation characteristics, (b) their normal frequency ranges, and (c) methods for measuring the intensity of the waves (one method for each type of wave). Simple block diagrams and only brief explanations of the methods are required.

5. (a) Explain why it should be possible to generate electrical power using either of the two nuclear reactions H + 31 H  → 42 He + 01 n , or

(i)

2 1

(ii)

235 92

U + 01 n  →

144 56

Ba +

90 36

Kr + 2 01 n .

(b) Which reaction process is currently being used in power-generating stations and why is the other, at present, not practical? (c) Sketch the basic structure of a nuclear power station, explaining the functions of (i)

the moderator,

(ii)

the control rods, and

(iii) the coolant. (d) State any TWO precautions which need to be taken to reduce possible radiation hazards to the staff working in such stations.


6. (a) inductance L

current I

resistance R

Key K

e.m.f. E

Figure 1

Write down a differential equation for the current I in the circuit in Figure 1 after the key K has been closed at a time t = 0, explaining clearly each term in the equation. (b) rotation axis perpendicular to paper

ω

magnetic field of uniform flux density B

starting position of coil (t = 0)

Figure 2 A coil of N turns, each of area A, is situated initially (at time t = 0) with the plane of the coil perpendicular to a magnetic filed of uniform flux density B. The coil is then rotated at a uniform angular velocity ω about an axis perpendicular to the magnetic field and passing through the centre of the coil, as shown in Figure 2. Derive an expression for the e.m.f. induced in the coil at any subsequent time t. (c) If the coil has an inductance L and a resistance R and the ends are connected together, write down the corresponding differential equation for the current I in the coil. Assuming a solution of the form I = P cos ωt + Q sin ωt, where P and Q are constants, determine expressions for P and Q in terms of B, A, N, ω, L and R. (d) Obtain a further expression for the time-averaged power loss in the coil due to Joule heating, and show that if ωL >> R, the power loss is independent of ω.

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1. (a) Describe briefly the important details of an experimental arrangement to accurately determine, by direct measurement, the variation of the extension of a metal wire produced by an increasing applied force to one end when the other end is fixed. (b) Instead of using direct measurement, a student has the idea that he can increase the accuracy of the measurements of the extensions of the loaded wire by measuring the change of electrical resistance of the wire. (i)

Assuming no change of cross-sectional area on stretching, show that theoretically, this is possible.

(ii)

Discuss the practicability of using this method with stainless steel wire of diameter 0.4 mm and resistivity ~ 10-6 Ω m, showing any necessary rough calculations.

(No circuit details are expected.) (c) By considering the expected (qualitative) results for the loading of the wire in (a), and also those for the compression of a solid metal block, suggest a possible explanatory molecular model sketching the implied variations of (i)

the potential energy and

(ii)

the force

between the molecules as their separation varies. significance of the main features of these variations.

Explain the physical

2. (a) State the principle of superposition for waves. Use this to explain the production of sound beats, and derive an expression for their frequency. (b) Use the principle of superposition to account for the observed phenomenon of interference, and state clearly the necessary physical conditions. Discuss the particular difficulties encountered in satisfying these conditions for normal light waves (not laser light), and state how these are overcome. (c) A rectangular wire frame is completely immersed in a soap solution and withdrawn carefully so that a soap film is stretched across the whole frame. Due to gravitational force and evaporation, the cross-section of the film will vary roughly with time as follows:


50 mm

(1) 1 minute

(2) 2 minutes

(3) 3 minutes

Figure 1

Give a qualitative account of what you would expect to observe during these 3 minutes if the film were illuminated by monochromatic light form behind the observer. Give brief explanations. (d) Suggest any one practical use for light interference (only brief details are required.)

3. (a) Faraday’s laws of electromagnetic induction may be summarised by the dφ equation E = − . dt Explain the physical meaning of this equation, using a coil of wire as an example. (b) Give brief details of one useful practical example of electromagnetic induction in a coil which involves (i)

movement of the coil;

(ii)

no movement of the coil.

(c) Explain the effect of electromagnetic induction on (i)

the switching-off of a current supply to an electromagnet; and

(ii)

the heating of a transformer core.

In each case, give a diagram showing the actual instantaneous direction of the induced e.m.f. (d) Briefly explain suitable precautions which can be taken to minimise the detrimental effects produced by the electromagnetic induction in (c) (i) and (c) (ii).


4. (a) Draw a diagram of a circuit you would use to determine the input-output d.c. voltage characteristic of an NPN transistor operating in the common emitter configuration. Give the approximate values of the resistances used in your circuit, explaining why they are used. (b) Draw a graph of a typical input-output voltage characteristic. With reference to this characteristic, explain the use of such a transistor for (i)

voltage amplification, and

(ii)

switching.

(c) Show how the simple transistor switching circuit can be used in (i)

a NOR gate, and

(ii)

an OR gate.

For each of these configurations give a truth table, and explain the logic of the possible operations.

5. (a) 3-dimensional model 'hill' (symmetric in horizontal plane)

B ball

r A ramp chute possible path of deflected ball Figure 2

In a gravitational analogue simulation of α-particle scattering by a thin metal sheet, balls are allowed to roll down a ramp chute on to a model ‘hill’ where they experience deflection, as in Figure 2. (i)

Explain the necessary variation of the profile (AB) of the ‘hill’ with the radius (r) of the horizontal cross-sections.

(ii)

Using this experimental arrangement how would you simulate the scattering of α-particles through different angles of deflection? Comment on the expected results.


(iii) Further explain how you would simulate the scattering of α-particles of various energies and state the expected results (qualitatively). (iv) Using this analogy, demonstrate how an upper limit to the size of a nucleus can be estimated. (v)

Suggest possible practical inadequacies of this gravitational analogue.

(b) Briefly describe the experimental evidence which convinced Chadwick that neutrons are neutral particles, similar in mass to protons.

6. (a) B a O

x

a

O

t= 0 P

Q y

A

ω

Figure 3

A point P moves in a circular path, around O as centre, with a constant angular velocity ω. (i)

Show that point Q, the projection of P on the diameter AB, moves with an acceleration towards O and that the magnitude of the acceleration is proportional to the displacement of Q from O. (O is the starting position for time t = 0.)

(ii)

Write down mathematical expressions for (1) the displacement of Q from O, (2) the velocity of Q, (3) the acceleration of Q, at any subsequent time t.

(iii) Hence, using the same time axis, plot the variations of (1), (2) and (3) with time during one complete cycle of motion of Q.


(b) If Q represents the location of a mass m suspended from a vertical hanging, light spiral spring which undergoes oscillations in a vertical plane, write down mathematical expressions for the variation with time of (i)

the kinetic energy, and

(ii)

the potential energy

of the system. (The mass of the spring should be ignored.) Plot the above time variations on a graph directly underneath the previous graph, using a similar scale for the time axis. (c) An additional S.H.M., acting along the x-direction, is now superimposed upon the original motion of Q, having the same amplitude a and angular velocity ω. (i)

Derive the equations of the resultant paths of motion of Q for the following conditions: (1) the phase difference between the two motions is zero, (2) the phase difference is π/2, (3) the phase difference is zero, but the angular velocity of the xdirection motion has increased to 2 ω.

(iii) For each condition, sketch the path traversed by Q, and indicate the direction of motion.

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1. (a) From a consideration of the flow of a liquid through a narrow tube, define the coefficient of viscosity in terms of the internal frictional force and determine its unit. (b) Explain how you would compare the viscosities of two liquids, deriving any mathematical relations required (Stokes’ Law may be assumed). Briefly indicate any necessary precautions or procedures for improving the accuracy of your measurements. (c) Explain the physical effects on your experimental measurements as the sizes of the ball-bearings were increased until their diameter became similar to that of the liquid container. (d) Distinguish between Newtonian and Non-Newtonian liquids, regarding their viscous behaviour, and give one example of each.

2. (a)

A spring is held vertically with a weight, attached to its lower end. It is made to oscillate vertically by a periodic up-and-down motion of the hand. On increasing the frequency of motion of the hand, it is observed that the amplitude of motion of the weight increases, becoming a maximum at a certain frequency. Give a brief qualitative explanation of this observation. As the frequency of motion of the hand increases, what other observations can be made about the phase between the driving force and the motion of the weight? (b) Consider the analogous physical system of an a.c. circuit, consisting of a coil and capacitor connected in series with a.c. voltage generator and, from first principles, derive the corresponding observable effects.


(c) Give one practical example each of resonance (either mechanical or electrical) which is (i)

useful,

(ii)

undesirable.

3. (a) Explain, by using wave-front diagrams, how the wave theory of light is able to explain (i)

the refraction, and

(ii)

the dispersion

of a narrow light beam incident upon the interface of two different optically transparent media. (b) Draw a diagram showing the ray paths through a prism spectrometer when a line spectrum is observed, and explain the necessary optical adjustments of the collimator and telescope. (c) Suggest possible advantages of replacing the prism by a diffraction grating.

4. (a) Using the rotating coil of a simple d.c. motor as an example, describe, with the aid of a diagram, the force effects of a magnetic field on an electrical current. (Details of the commutator are not required.) (b) Briefly explain electrical conduction in metals. (c) Account for the production of a Hall voltage when a thin strip of a conducting material, carrying a current, is placed in a magnetic field. (d) Derive an expression for the Hall voltage and indicate the various physical factors which may be adjusted to ensure (i)

high sensitivity, and

(ii)

good spatial resolution

in a Hall probe used for measuring magnetic fields.


5. (a) Compare the physical means of production of electromagnetic waves by (i)

a gas discharge tube, and

(ii)

an X-ray tube.

Describe the main differences between the emitted spectra and how these can be explained by the different internal atomic processes which occur. (b) Briefly indicate how X-rays may be used to determine the separation of atomic planes in a crystal.

6. (a) Consider a satellite of mass m moving in a circular orbit of radius r around an assumed homogeneous spherical earth of mass M and radius R. (i)

Show that the period T of the satellite for a complete orbit is proportional to r3/2.

(ii)

Derive an expression for the total energy of the satellite in terms of the given parameters, together with G, the gravitational constant.

(b) Due to the friction of the earth’s atmosphere the satellite experiences a drag force Cρv², where ρ is the density of the atmosphere and v is the speed of the satellite, C being a constant. (i)

Explain why the speed v of the satellite would be expected to increase with time, t.

(ii)

From a consideration of the work done by the drag force and the rate of loss of energy of the satellite, show that dr/dt = -2ρCvr/m.

(iii) Assuming that (dr/dt) changes slowly and may be considered constant over one orbit show that the small fractional change in period time is given by ∆T/T = 6πρCr/m. (iv) Describe the path taken by the satellite, explaining what, finally, should happen to it.

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1. (a) Write down Newton’s second law of motion. Apply it to the situation where a body, initially at rest, is subject to a constant force, and describe the subsequent motion. (2 marks) (b) Clearly distinguish between the properties ‘mass’ and ‘weight’ of a body and explain why a passenger sometimes has the feeling of ‘weightlessness’ in a lift. (5 marks) (c) Without giving any mathematical derivations, explain how it is possible for a body to move with constant speed in a horizontal circular path. (2 marks) (d) Describe an experiment to demonstrate the relation between the angular velocity of the body in (c) and the radius of the path, for a constant acting force, explaining any source of error. (7 marks)

2. (a) Qualitatively compare the molecular/atomic models for (i)

a gas and

(ii)

a solid

with particular reference to the forces exerted by the molecules/atoms, and the effects of an increase in temperature. (8 marks) (b) Briefly describe the origins of the following binding forces in solids: (i)

ionic (electrostatic) binding,

(ii)

metallic binding and

(iii) covalent binding. (4 marks) (c) Glass reinforced plastic (fibre glass) is made up of glass fibres embedded in plastic material. Explain its mechanical advantages over conventional metals. (4 marks)

3. Both light and sound can be considered as wave propagations of energy. (a) Carefully compare the main characteristics of such waves and their propagation. (10 marks)


(b) Distinguish between (i)

refraction and

(ii)

diffraction

for a sound wave, giving one practical example of each.

(4 marks)

(c) Briefly explain why diffraction is more difficult to observe in ‘everyday life’ for light rather than sound. (2 marks)

4. (a) Describe the phenomenon of electromagnetic induction under the following conditions: (i)

physical movement is involved;

(ii)

no physical movement is involved. (3 marks)

(b) Describe the analogous resulting effects when a battery is connected in turn across circuits consisting of (i)

an inductor and resistor in series, and

(ii)

an uncharged capacitor and resistor, in series.

A full mathematical analysis is only expected for (ii).

(9 marks)

(c) A fully-charged capacitor is suddenly connected across a coil of large inductance. Explain, qualitatively, the waveform you would expect to observe in an oscilloscope connected across the coil, and how the stored energy changes with time. (4 marks)

5. (a) Account for the exponential time decay of a radioactive isotope.

(3 marks)

(b) Uranium 238 decays to Uranium 234 as follows: 238 92

α U  → Th  β → Pa  β →

234

U,

where α and β represent accompanying α-, β-particle emissions. Determine the missing atomic number and mass number values, giving explanations of your choices. (3 marks) (c) Natural radium is known to emit α-particles and β-particles and also γphotons. Explain how you would verify this experimentally using a method based upon absorption. (5 marks)


(d) Mention the most important factors which determine the dangerousness of a sealed radioactive source, used externally, and the main precautions to be taken when using it. (5 marks) 6. (a) An alternating current I = I0 sin ωt flows in the following circuits: (i)

an inductance L and resistance R connected in series,

(ii)

a capacitance C and resistance R connected in series.

In each case, determine from first principles the reactance and the phase relation between the voltage across the reactive element and the current. (4 marks) (b) Hence, using a phasor diagram, obtain an expression for the impedance of a circuit consisting of an inductance L, a capacitance C and a resistance R connected in series with an a.c. source. (2 marks) (c) For the circuit of (b) the current is a maximum at the resonant frequency ω0. Show that the power taken by such a circuit drops by 50% of that taken at resonance when the frequency is changed to ω, where ωL −

1 =R ωC

(3 marks)

(d) By writing ω as (ω0 + ∆ω) show that ∆ω ~ R/(2L). (You may consider ∆ω << (3 marks) ω0.) (e) The ‘sharpness’ of the resonance is given by Q = ω0/(2 ∆ω) and it is usual for Q ~ 30. (i)

Show that at resonance the r.m.s. voltage across the capacitor C will be Q × r.m.s. voltage across the whole circuit.

(ii)

Explain how this is possible. (4 marks)

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1. (a) Explain in terms of molecular forces why (i)

it is possible to ‘float’ a small steel needle on the surface of water,

(ii)

if part of the needle is inserted vertically into the water some of the water is drawn up around it above the normal water level, and

(iii) a liquid film always assumes a minimum surface area. For (i) and (ii) diagrams should be drawn showing the relevant forces. (8 marks)

(b) Discuss the effect of the spreading of a liquid on a solid surface and give one practical example, each, where (i)

good spreading,

(ii)

poor spreading

is important.

(3 marks)

(c) Briefly describe a method for measuring the surface tension of water using the rise of water in a glass capillary tube. Derive any necessary relation and point out necessary experimental precautions. (5 marks)

2. (a) The human eye functions as a converging lens of variable focal length. Explain why the apparent sizes of the Moon and a dollar held at arm’s length seem similar. (2 marks) (b) When a single converging lens is used as a magnifying glass the viewed image may be formed at (i)

infinity or

(ii)

the distance of nearest clear vision from the eye.

Using a ray diagram show which of these arrangements gives the greatest magnification. What is the physical factor limiting the magnification? (4 marks)


(c) Show, using a ray diagram, that it is possible to further increase the magnification by using an additional converging lens. (No mathematical treatment involving the lens equation is required.) (3 marks) (d) Give reasons why the brightness of an image recorded on photographic film in a simple camera is proportional to d 2 t / f 2 , where d is the aperture diameter, t the time exposure and f the focal length of the converging lens. Hence explain the meaning of f-stop, and its use in photography. (7 marks)

3. (a) A long slinky spring is laid flat on a horizontal table and slightly stretched. Briefly explain how you would produce two transverse pulses moving along the spring in opposite directions from each end, when the amplitudes are (i)

in the same direction and

(ii)

in opposite directions.

Draw suitable diagrams showing the propagation of the pulses along the spring, through its centre. (4 marks) (b) By reference to the results of (a) explain the main effects of the principle of superposition on interfering waves. (2 marks) (c) Describe, qualitatively, the phenomenon of wave interference and give one example, each, for (i)

sound and

(ii)

light,

which may be experienced in daily life. (No mathematical derivations are required.) (5 marks) (d) Explain clearly the necessary conditions for observable interference to take place between (i)

sound waves and

(ii)

light waves,

briefly contrasting any main difficulties encountered in satisfying such conditions. (5 marks)


4. (a) An electrical circuit consists of a resistor connected across the terminals of a battery. By considering the charges moving around the circuit, define the terms (i)

electric field,

(ii)

potential difference and

(iii) electromotive force (e.m.f.). (4 marks) (b) Explain the mechanism by which heat would be produced in the resistor. (2 marks) (c) Obtain an expression for the rate of heat dissipation in the resistor in terms of the electric current and resistance. Explain clearly the differences in computing the rate of heat dissipation in an a.c. circuit which includes a reactive element. (3 marks) (d) Briefly describe the public electrical power transmission system, usually adopted, from the power station to the domestic consumer. Explain why such a system is used. (4 marks) (e) By considering the resistance of the transmission cables and of the appliances used locally, explain why the mains voltage varies significantly throughout Hong Kong, and why there are variations at any particular location. (3 marks)

5. (a) Compare the appropriate physical conservation laws which apply to (i)

elastic and

(ii)

non-elastic

collisions between a moving non-rotating body and a stationary body. (3 marks) (b) Give brief accounts of the following collisions, explaining whether they are elastic or non-elastic: (i)

high energy α-particle scattering by atoms in thin metal foils.

(ii)

slow neutron bombardment of 235U atoms.

(iii) high energy electron collisions with gaseous xenon atoms. (7 marks)


(c) Describe the Franck-Hertz experimental investigation of the effect of varying the electron energy in (iii) and briefly explain the importance of the results. (6 marks)

6. (a) By considering the uniform motion of a point in a circular path, demonstrate the meaning of simple harmonic motion (S.H.M.), giving a relation between the acceleration and displacement from the equilibrium position for a particle undergoing S.H.M. (3 marks) (b) Briefly explain how it is possible to set a small object into S.H.M. using a spiral spring. (3 marks) (c) Atoms of a diatomic molecule (each of mass m) are able to oscillate towards and away from each other in a similar manner to two small objects connected by a spiral spring. Assume that the potential energy of such a system, for an atomic spacing x, is U = -(a/x) + [b/(2x²)], where a and b are constants. (i)

Obtain an expression for the corresponding force F between the two atoms and determine the equilibrium separation in terms of a and b. Sketch out the variation of F with x, explaining the shape and significant features of your graph.

(ii)

Show that for small oscillations about the equilibrium location of the atoms (you may consider one atom to remain stationary and the effective mass of the other atom to be m/2), S.H.M. occurs and obtain expressions for (I) the force constant (force/displacement) and (II) the oscillation period. (Hint: use binomial expansion for terms in the force equation.) (10 marks)

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1. (a) State the main assumptions of the kinetic theory as applied to an ideal gas, briefly explaining the pressure exerted by a gas on its container (no mathematical derivation expected). (5 marks) (b) Point out the main observed differences in the behaviour of real gases compared with an ideal gas, giving explanations, using p-V characteristics. Comment on the differences in behaviour at high pressures and low temperatures. (7 marks) (c) Distinguish between the processes of evaporation and boiling for a liquid, with reference to unsaturated and saturated vapours. (4 marks)

2. (a) Discuss qualitatively the motion of a small metal ball allowed to drop downwards into a long vertical tube of liquid so that it moves along the axis of the tube (radius of tube >> radius of ball). (3 marks) (b) Derive Bernoulli’s equation, P + hρg + ½ρv² = a constant for the flow of a fluid through a tube of varying cross-sectional area. Clearly explain all the physical parameters used in this equation. (6 marks) (c) In practice, discuss the likely sources of error in applying Bernoulli’s equation to the flow of (i)

liquids, and

(ii)

gases

in tubes.

(3 marks)


3. (a) Describe the main characteristics of light when considered as (i)

a wave propagation, and

(ii)

moving particles. (5 marks)

(b) Give a brief account of an experiment which illustrates the wave nature of light AND a second experiment which illustrates its particle nature (no mathematical derivations expected). (9 marks) (c) Explain how it is possible to reconcile the wave/particle nature of electrons. (2 marks)

4. (a) Give the theory of the production of an a.c. voltage by a plane coil rotating in a uniform magnetic field, identifying the maximum and zero voltages with the positions of the coil. (5 marks) (b) Draw a diagram of the circuit of a d.c. power pack used for generating a variable d.c. voltage from the a.c. mains, giving rough values for any inductors, capacitors and resistors used. (3 marks) (c) With reference to your circuit in (b), briefly explain the physical principles involved in (i)

the transformer (working under ideal conditions),

(ii)

the full-wave rectification process, and

(iii) the filter. For (iii) explain your choice of the values of any inductances, capacitances and resistances. (8 marks)


5. (a) Radioactive elements occur in nature. Summarise their unique characteristics, including how their activity decays. (4 marks) (b) Describe an experiment, performable in a school laboratory, to measure a radioactive half-life. (8 marks) (c) Explain the method of archeological dating using carbon-14.

(4 marks)

6. (a) Derive, from first principles, expressions for the energies stored by (i)

a pure capacitor of capacitance C charged by a voltage V0, and

(ii)

a pure inductor of inductance L through which a current I0 flows. (5 marks)

(b) The charged capacitor in (a)(i) is isolated and then connected across the inductor in (a)(ii). Show that the charge on the capacitor varies with subsequent time t as Q = Q0 cos ω0t, and obtain a value for ω0. (4 marks) (c) Draw a phasor diagram for a series LCR circuit connected across a signal generator of voltage V = V0 cos ωt. Derive the condition for the maximum stored energies of the inductor and the capacitor to be the same. (5 marks) (d) With reference to the stored energies, compare the two physical situations described in parts (b) and (c). (2 marks)

- End of Paper -



1. (a) Describe simple harmonic motion (s.h.m.).

(2 marks)

(b) A simple pendulum consisting of a weight suspended vertically by a string, of length l, attached to a fixed point is set in motion in a vertical plane, the amplitude of oscillations being small. Show that the motion is simple harmonic and write down expressions for the displacement, velocity and acceleration of the weight after a time t. Sketch the variations of potential and kinetic energies with time. (6 marks) (c) Describe an experiment to verify that such a pendulum undergoes s.h.m. (6 marks) (d) A student decides to use the oscillation of such a pendulum to obtain a value for the free-fall acceleration due to gravity. Without describing this experiment, critically discuss TWO possible sources of error in your measurement. (2 marks)

2. (a) Distinguish between heat and internal energy and explain their connection with the temperature of a body. (3 marks) (b) Briefly discuss the differences in physical nature between the internal energy for a gas and a solid. (4 marks) (c) Describe the use of a constant volume gas thermometer to accurately measure temperature, and explain how this leads to the concept of an absolute zero temperature. (7 marks) (d) Explain why there may be disagreement in temperature measurements between thermometers using different physical thermometirc properties. (2 marks)

3. (a) Explain the formation of stationary waves along a stretched wire which vibrates with a frequency f and is fixed at both ends, giving graphical representations of the motion amplitude at different positions along the wire corresponding to time intervals of 1/(4f). What are the appropriate conditions for such stationary waves to occur? (5 marks)


(b) Suggest a possible experimental method for demonstrating such stationary waves and determining the necessary conditions. (2 marks) (c) Using this as an example explain the meaning of resonance. Briefly explain how such a phenomenon could occur and be observed in (i)

an a.c. electrical circuit, and

(ii)

atoms.

[No theoretical derivations required.]

(9 marks)

4. (a) Two long parallel wire, each of length l and separated by a distance d, carry a current I in the same direction. Draw a diagram of this arrangement and on it show (i)

the magnetic field at each wire due to the other, and

(ii)

the corresponding forces.

giving their magnitudes.

(3 marks)

(b) How may a similar arrangement be used to define the ampere unit of current? (1 mark) (c) Using suitable diagrams, explain the working of a simple d.c. motor, where the magnetic field is produced by a permanent magnet. (4 marks) (d) For this motor explain, in detail, the observed sequence of physical effects of (i)

switching it on with no mechanical load and,

(ii)

after a while, applying such a load. (8 marks)

5. (a) Compare the production and maintenance of electrical current flow in a circuit formed by the connection of (i)

a resistance, and

(ii)

a heated cathode diode,


across a variable d.c. voltage power supply. What are the main effects of varying the output voltage? processes involved should be explained.

All physical (9 marks)

(b) Explain the use of an electron beam in a cathode ray oscilloscope. Give a diagram showing the d.c. electrical connections but no details of the beam focussing or electronic circuits are expected. (5 marks) (c) Suggest a possible hazard of sitting too near a colour television, giving a brief explanation. (2 marks)

6. (a) Derive an expression for the force experienced by an object of mass m which is rotating with angular velocity ω around a circular path of radius r, in the absence of any gravitational field. (4 marks) (b) In a laboratory a small weight is attached by a piece of string of length l to a fixed point and set into circular motion in a horizontal plane. Derive an expression for the angle of inclination of the string with the vertical, explaining what happens as ω is increased to a high value. (3 marks) (c) A closed tube containing a mixture of two liquids of densities ρ and ρ’ (ρ > ρ’) is attached at the end by a hinge (allowing vertical motion) to a rigid rod. If this rod, and also the tube, is rapidly rotated in a horizontal plane with an angular velocity ω, compare the excess forces on a small elemental volume A∆r of each liquid at distance r from the centre of motion (A being the area of cross-section of the tube). Hence explain the action of a centrifuge. (5 marks) (d) A students argues that there is no need to use a centrifuge to separate the two liquids since if the mixture is just left stationary they will separate under the force of gravity. Compare the excess forces using each method and comment on the statement of the student. (4 marks)

- End of paper -



1. (a) Derive an expression for the kinetic energy of a body of mass m, and hence explain its meaning, by considering the body to be linearly accelerated from rest to a velocity v. (2 marks) (b) Show that an analogy exists for rotational motion and hence define the physical quantity ‘moment of inertia’. (3 marks) (c) How would your differentiate experimentally between a hollow and a solid cylinder, which both have the same dimensions and mass? Give the theory of your method. (4 marks) (d) Describe, and give the theory of, an experiment to measure the moment of the inertia of a flywheel. (7 marks)

2. (a) Briefly distinguish between the different types of strongly attractive forces which bond atoms of materials together. (6 marks) (b) Taking into consideration the resistance of solids to deformation by external forces, sketch the expected variations of (1) the interatomic force and (2) the potential energy against the separation of two atoms in a solid. (4 marks) (c) (i)

(ii)

Sketch the expected variations of stress against strain for (1) a copper wire, (2) a rubber band and (3) a glass fibre in a Young modulus experiment, the loading being increased to just before the materials break. Briefly account for the different behaviour of the materials. (6 marks)

3. (a) By considering the propagation of light waves through slit(s), carefully distinguish between diffraction and interference. (7 marks) (b) Explain why interference of light is not observed when (i)

two separate light sources are used and

(ii)

the path difference between light rays from the same light source is too great. (4 marks)


(c) Draw a diagram showing what you would expect to observe when viewing through a diffraction gating the vertical glowing filament of an electric lamp, placed several meters away. The grating is placed with its ruled lines parallel to the filament. Briefly explain the observations you make. (5 marks)

4. (a) An a.c. voltage supply is connected across a coil of many turns, this coil being placed over the vertical iron rod of a retort stand and resting on the base. Explain clearly your expected observations, and the physical principles involved when (i)

a small aluminium ring is dropped over and slides down the vertical rod of the retort stand,

(ii)

the ring of (i) is replaced by a similar ring, but broken by a vertical slot and

(iii) the ring of (i) is fastened down on top of the coil. (6 marks) (b) A series circuit is formed from a coil of inductance 500 H, a 2 V light bulb, an open switch and a 2 V battery. Explain your expected observations when (i)

the switch is closed and

(ii)

after connecting a neon lamp across the coil, the switch is opened. (4 marks)

(c) Draw a circuit which can be used to observe the periodic variations of current I together with those of an applied a.c. voltage V for the coil of (b). Explain mathematically the phase difference you would expect between I and V. (6 marks) 5. (a) Explain how you would distinguish experimentally between α, β and γradiating radioactive sources using a Geiger-muller counter detection system. (6 marks) (b) What changes take place in the constituents of the nuclei when such radiations are emitted? (3 marks)


(c) Explain your choice of type of radiation source, giving brief details of use for (i)

monitoring paper thickness, during manufacture,

(ii)

estimating the size of nuclei and

(iii) treating body cancer by destroying cancer cells. (7 marks)

6. (a) An initially uncharged capacitor of capacitance C is connected in series with a resistor of resistance R. The capacitor is now fully charged up by connecting a battery of e.m.f. E across this combination. (i)

(ii)

dQ = A − BQ , where Q is the charge stored in the dt capacitor after the battery has been connected for a time t. Determine the constants A and B in the above equation. Derive an equation

Solve this equation for Q and sketch the variation of Q with t. Give physical explanations of the variation.

(iii) From first principles determine the total work done by the battery in fully charging up C and the final energy stored in C. Explain, and account for mathematically, any difference between these. (11 marks) (b) (i)

Write down an analogous equation to that of (a)(i) for the velocity v of a ball bearing of radius a and mass m falling vertically, from rest, in a viscous liquid after an elapsed time t. The effect of the buoyancy of the liquid should be neglected.

(ii)

Solve the equation for v and sketch the variation of v with t. Give physical explanations of the variation. (5 marks)

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1. (a) Explain the meanings of Newton’s second and third Laws of Motion. (3 marks) (b) Apply these laws to the rapid impact between two bodies, which were initially moving with unequal velocities along the same direction, and show that linear momentum is conserved. Explain whether the total kinetic energy is necessarily conserved, or not. (7 marks) (c) Briefly discuss the conservation of energy in regard to (i)

the results of the Franck-Hertz experiment and

(ii)

the energy spectrum of the β-particles emitted naturally by some nuclei.

(No experimental circuit details or theoretical details are expected.) (6 marks)

2. (a) State the main assumptions of Kinetic Theory as applied to ideal gases. (4 marks) (b) (i)

Explain why the speed of diffusion of a gas is much slower than the average speed of the gas molecules.

(ii)

Distinguish between the average separation of the molecules and their mean free path. (4 marks)

(c) (i)

Briefly describe an experiment for measuring the rate of diffusion of bromine into air and hence show how to estimate the mean free path of bromine molecules. (Random walk statistical rule to be assumed and density of bromine known.)

(ii)

By a consideration of the effect of diffusion on the various constituents of the earth’s atmosphere, briefly discuss how you would expect the composition to vary with height. Assume no convection or turbulence. (8 marks)


3. (a) Demonstrate the differences between (i)

transverse wave propagation,

(ii)

longitudinal wave propagation,

by drawing graphical plots showing the corresponding variations of the displacements of the medium particles with distance from the source for times (8 marks) t = 0, T/4. T/2 and 3T/4, where T is the wave period. (b) Describe an experiment to show the phase change of the particle oscillations with distance from a sound wave source, and hence explain how you would determine the wave propagation speed. (6 marks) (c) How does the propagation of light waves differ from that of sound waves? (2 marks)

4. (a) Give definitions of (i)

the electric field intensity and

(ii)

the electric potential,

and explain the relationship between them with the aid of a diagram showing equi-potential lines. (4 marks) (b) Explain the concept of capacitance by considering a small charged metal sphere, assuming the inverse square law for the force between charges. (4 marks) (c) Describe how you would experimentally investigate the geometric factors affecting the capacitance of a parallel plate capacitor using a reed switch to convert the stored charge into a current. (There is no need to explain the working of the reed switch.) Suggest two sources of error. (8 marks)

5. By considering the force on free electrons of charge -e moving with a constant velocity v in a path, perpendicular to a uniform magnetic field B, (a) explain the production of an electric field E when an electric current is passed through an n-type semiconductor crystal in a direction perpendicular to a magnetic field B. (5 marks) (b) further, explain the production of another electric field E’ in a linear conductor moved perpendicular to the magnetic field B. (4 marks)


(c) describe an experiment to measure the charge/mass (e/m) ratio for electrons using an electric field and magnetic field perpendicular to each other. (No theory of the production of the magnetic field is expected.) Briefly indicate main difficulties. (7 marks) 6. (a) Define simple harmonic motion (s.h.m.) and give one example of motion approximating to s.h.m. which may be observed during our daily lives. (2 marks) (b) (i)

A long spiral spring of force constant k hangs vertically from a fixed support with a weight of mass m attached to its bottom end. If the weight is pulled downwards and then released show that the subsequent motion is s.h.m., with the displacement from the equilibrium position at any time t given by x = a cos ω0 t, where a is a constant and ω0 the natural angular frequency of oscillation.

(ii)

If the weight now moves in a viscous liquid, there will be an additional dx dx is the instantaneous retardation force acting of b , where dt dt velocity. Write down the new equation of motion. Assume a solution, x = Ae-γtcos ωt and by substitution derive an expression for γ and show that the new angular frequency of oscillation, ω = (ω20 − γ 2 )1/ 2 . (Hint: π .) consider particular times t = 0, 2ω (10 marks)

(c) Now consider the connection of a charged capacitor of capacitance C across a coil of inductance L and resistance R. Show that a similar differential equation holds good for the charge Q on the capacitor, in place of the displacement x in (b)(ii), and hence by analogy determine the corresponding expression for γ, ω and ω0. (4 marks)

- End of Paper -


HONG KONG ADVANCED LEVEL EXAMINATION AL PHYSICS 1993 Essay Type Question 1. (a) State the differences between a steady flow and a turbulent flow of fluids. (3 marks) (b) In the steady flow of a liquid through a narrow pipe, explain how a velocity gradient is set up. (3 marks) (c) A block of base area A lies on a horizontal lubricated floor. The lubricant is a layer of liquid having thickness t and coefficient of viscosity η. Derive the force required to move the block at a constant velocity v. Briefly explain each step in your argument and state the assumption(s) you made. (4 marks) (d) The viscosity of a liquid can be measured by using Stokes’ law. Ball-bearings are dropped into a long vertical glass tube containing the liquid and their respective terminal velocities are measured for calculating the coefficient of viscosity of the liquid. State and explain the precautions in performing this experiment. (No mathematical derivation is expected.) (6 marks)

2. (a) Describe FOUR contrasting features of progressive and stationary waves, and state the conditions necessary for a stationary wave. (6 marks) (b) Beats can be heard when a tuning fork and a guitar string vibrate simultaneously with slightly different frequencies f1 and f2 respectively. (i)

With the aid of diagrams, explain how beats are formed. diagram to show the resulting wave form.

Draw a

(ii)

Show that the beat frequency is equal to the difference between f1 and f2. (7 marks)

(c) Briefly describe how the principle of beats would be used to detect the speed of cars in a police radar speed check system. (No mathematical derivation is expected.) (3 marks)

3. (a) State the order of magnitude of (i)

the average drift velocity of electrons in a current-carrying wire;

(ii)

the speed of electrical signals in a circuit.

Account for the difference by explaining the average drift velocity of electrons and the speed of electrical signal in a circuit. (5 marks)


(b) Derive the current flow equation i = nAve fro a metal wire. Explain the meanings of the symbols in the equation. (3 marks) (c) Draw a labelled diagram of a moving-coil meter. Briefly describe its working principles and explain how a linear scale may be achieved. (8 marks)

4. (a) Explain each of the three terms in Einstein’s photoelectric equation ½mvm² = hν - φ. (2 marks) (b) Figure 4.1 illustrates the basic features of the laboratory apparatus for investigating photoelectricity. It contains a vacuum photoelectric cell P with a photosensitive metal C of large area and a collector of electrons D. incident monochromatic radiation P C Figure 4.1

D

A ammeter

V voltmeter

battery

(i)

Sketch a graph showing the dependence of the current i through the ammeter on the potential difference V (V = potential of D - potential of C). Your graph should cover both positive and negative values of V. Briefly explain the shape of your graph.

(ii)

Copy the graph you have drawn in (i) and sketch on it the curves for (I) increased light intensity, with the light frequency being kept constant; (II) increased light frequency, with the light intensity being kept constant. Explain briefly.

(9 marks)

(c) Briefly describe the use of photoelectric cells in the reproduction of sound from film soundtracks. (2 marks) (d) Photoelectric emission is one of the phenomena that demonstrate the particlelike properties of electromagnetic radiation. Briefly describe an experiment to show that particles such as electrons also exhibit wave-like properties. (3 marks)


5. (a) (i)

Briefly describe an experiment to investigate the r.m.s. current in an LRC series circuit for different frequencies of an a.c. supply. (No mathematical derivation is expected.)

(ii)

Sketch a graph showing how the r.m.s. current in the circuit varies with the applied frequency. Account for the shape of the curve with the aid of phasor diagrams.

(iii) Sketch, on the same graph in (ii), the curves for (I) smaller resistance; (II) larger resistance. (11 marks) (b) Figure 5.1 shows a simplified tuning circuit for radio receivers. Aerial

Figure 5.1

C

L ,R

To receiver

Earth

(i)

Explain its operation.

(ii)

Suggest a method to improve the reception performance of the circuit. Explain briefly. (5 marks)

6. (a) An ideal spring of force constant k is mounted horizontally with one end fixed and the other end attached to a block of mass m (as shown). The block is set to oscillate with amplitude A on a level, frictionless surface. block Figure 6.1

fixed end

spring

m x

(i)

Sketch a graph of elastic potential energy U against x for the spring-mass system, where x is the distance of the block from the fixed end. Mark on the graph the position xc of the central point of the oscillatory motion.


(ii)

On the same graph in (i), use a dotted line to sketch the graph of kinetic energy of the system against x. Briefly explain your graph by using energy-based arguments. (4 marks)

(b) In (a), the spring is assumed to have negligible mass. However, no spring is completely massless. To find the effect of the spring’s mass, consider a spring of mass M and force constant k. When the spring is stretched or compressed by an amount e, the elastic potential energy is ½ke². (i)

Suppose at a certain instant, the speed of the block is v and the length of the spring is L. For each spring element, its speed is proportional to its distance l from the end. Show that the kinetic energy of the spring is Mv²/6. (Assume uniform mass distribution of the spring.) (Hint: find the mass of the speed of each spring element of length dl.)

(ii)

Find the extension of the spring in terms of x and write down the expression for the total energy of such an oscillating spring-mass system. Take the time derivative of the expression and find the period of the subsequent motion. (10 marks)

(c) How does the motion change if the oscillating system is immersed in water? (2 marks)

- End of Paper -



1. (a) Figure 1.1 shows a car travelling over a hump which is an arc of a vertical circle. Compared with travelling on a level road, would a passenger feel heavier, lighter or the same as usual when the car passes the top of the hump? Briefly explain your answer. (Assume that the passenger remains in contact with the seat) (3 marks)

Figure 1.1

(b) State the factors on which the moment of inertia of a body depends. Compare the role of the moment of inertia in rotational motion with the role of mass in linear motion.(5 marks) (c) A man, with his arms stretched out, is standing at the centre of a light, horizontal circular platform which can rotate freely about its vertical axis. He and the platform are then set into rotation. Explain what happens if he puts down his arms. Discuss whether there is a change in his kinetic energy. (5 marks) (d) Two identical cylinders, A and B, are held with their axes horizontal and at the same height on slopes of the same inclination. When released from rest, cylinder A slides down a smooth slope while cylinder B rolls down a rough slope without slipping. By using the principle of conservation of energy, explain which cylinder has the greater linear speed when reaching the bottom of the slopes. (No mathematical derivation is required) (3 marks)

2. (a) State Huygens’ principle. With the aid of the diagrams, use the principle to explain (i)

how the direction of propagation of a plane wave is related to the wavefront;

(ii)

why plane waves refract as they pass from one medium to another. (7 marks)


(b) (i)

Explain why interference patterns cannot be successfully produced with too small, close light sources.

(ii)

Explain, with the aid of a diagram, how the pattern in (i) is overcome in Young’s experiment.

(iii) Describe and account for the observed interference pattern. (7 marks) (c) Describe and explain one practical use for light interference.

(2 marks)

3. (a) (i)

Solids can be thought of as networks of atoms connected by ‘small springs’. Explain how this method can be deduced from solids’ observed resistance to deformation.

(ii)

Sketch the curve of potential energy against interatomic separation and use it to explain the phenomenon of thermal expansion of solids. (6 marks)

(b) Glass is a strong, stiff and brittle material. Sketch the stress-strain graph for glass and briefly explain why it is so described. (3 marks) (c) With suitable diagrams, use the Bernoulli principle to explain (i)

how a yacht can sail against the wind;

(ii)

the curved flight of a spinning ball. Also suggest one design feature which increases the curvature of the ball’s flight. (7 marks)

4. (a) (i)

Magnetic fields are usually described in terms of magnetic field lines. Use this concept to explain the term ‘magnetic flux density’.

(ii)

State the factor(s) which determine(s) the total flux linkage for a plane coil placed in a uniform magnetic field. (3 marks)

(b) (i)

With a suitable diagram, explain qualitatively the working principles of a Hall probe.

(ii)

Briefly describe an experiment to investigate the variation of magnetic flux density along the axis of a solenoid by using a Hall probe. State any precaution(s) needed in the experiment. (9 marks)


(c) Explain, by means of the laws of electromagnetic induction, how a search coil can be used to investigate the flux density of an alternating magnetic field. (No mathematical derivation is required) (4 marks)

5. (a) (i) (ii)

What is meant by the ‘binding energy’ of a nucleus? Sketch a graph of binding energy per nucleon against mass number and use it to explain why (I) a 235U nucleus is not as stable as a 56Fe nucleus; and (II) a nucleus of mass number 200 readily undergoes fission but a nucleus of mass number 20 does not. (7 marks)

(b) (i)

For a nuclear fission reactor in normal operation, nuclear fissions must be controlled so that on average only one neutron from each fission produces another fission. Explain why this is necessary.

(ii)

Give two components of a nuclear fission reactor which are responsible for controlling the number of neutrons producing further fissions. Briefly describe their actions. (5 marks)

(c) (i)

State two advantages of using fusion as a source of energy, compared with using fission.

(ii)

Give the reason(s) for hindering the practical use of controlled fusion as a source of energy. (4 marks)

- End of Paper -



1. (a) In each of the following situations, use Newton’s law of motion to explain whether or not a net force is acting on the body. If no net force is acting, describe how the forces are balanced. If a net force is acting, explain the origin of the net force and state its direction. (i)

A raindrop which falls at terminal speed.

(ii)

A ping pong ball which collides obliquely with a smooth wall.

(iii) A communications satellite which maintains a constant position above the earth’s surface. (8 marks) (b) A rubber ball is dropped freely from a certain height onto a horizontal floor. It rebounds to the same height after each bounce. In terms of the force acting, state two ways in which the motion, although periodic, differs from simple harmonic motion. (4 marks) (c) (i)

For a planet revolving round the sun in a circular orbit of radius r and with period T, show that r3 = KT2 where K is a constant.

(ii)

Is the equation r3 = KT2, with the same constant K for the planet, also valid for a satellite circling round the earth? Explain briefly. (4 marks)

2. (a) In terms of the kinetic theory model of gases, explain: (i)

what an ideal gas is,

(ii)

how gases exert pressure on the walls of their containers,

(iii) why compressing a gas increases its temperature. (7 marks) (b) Explain why some of the assumptions of the kinetic theory of an ideal gas could not be applied to real gases at high pressures or low temperatures. (4 marks)


(c) Quantitatively, the first law of thermodynamics can be stated as: ∆Q = ∆U + ∆W (i)

Explain this relationship in words.

(ii)

‘A compressed gas in a hollow, steel cylinder expands and lifts a weight; it cools in the process and is then heated by conduction through the cylinder.’ Describe the above change in terms of the first law of thermodynamics and hence explain whether you can determine that there has been any change in internal energy of the gas. (5 marks)

3. (a) Unpolarised sunlight is incident horizontally on air molecules around O in the earth’s atmosphere. Part of the light is transmitted horizontally and part is scattered vertically downward. y

unpolarised sunlight air molecules

transmitted light

0 z

scattered light

x

Briefly explain which ray, the transmitted one or the scattered one, is plane polarised and give the direction of the electric field vector for this ray. Describe a method to identify this polarised light ray. (5 marks) (b) Give an account of an everyday example involving polarised light.

(3 marks)

(c) (i)

State two differences between laser light and light emitted by a light bulb.

(ii)

What is meant by ‘population inversion’? How do gas lasers rely on this to operate?

(iii) State and explain two advantages of using laser for cutting over mechanical devices. (8 marks)


4. (a) With the aid of a circuit diagram, briefly describe how a reed switch works in investigating the dependence of the charge stored in a parallel-plate capacitor on (i)

the area of overlap of the plates, and

(ii)

the separation between the plates.

Show graphically the expected results.

(8 marks)

(b) What is the physical meaning of the reactance of a capacitor? On what factors does the reactance of a capacitor depend? (2 marks) (c) Briefly explain the actions of the two capacitors and the inductor in the following smoothing circuit. (6 marks) L + rectified unsmoothed p.d. _

+ C1

C2

d.c. output _

5. (a) Describe an experiment for measuring the wavelength of monochromatic light using a spectrometer and a diffraction grating with a known grating spacing. (4 marks) (b) A spectrometer together with a diffraction grating can also be used to observe the line emission spectrum from a hydrogen discharge tube. (i)

Explain why hydrogen atoms emit light only of discrete wavelengths.

(ii)

How does this kind of spectrum differ from a line absorption spectrum? Explain how an absorption spectrum can be formed. (5 marks)

(c) (i)

Sketch a graph of a typical X-ray spectrum, and explain how the characteristic and continuous parts of the spectrum are formed.

(ii)

Why is there a definite minimum wavelength of the X-rays produced? (7 marks)

- End of Paper -



1. (a) The centripetal acceleration, a, of a body undergoing a uniform circular motion v2 of radius r can be expressed as either (1) a = or (2) a = ω 2r, where v and ω r are linear and angular speeds of the body respectively. For a uniform circular motion of constant period, student A thinks that a decreases with r according to equation (1), while student B argues that a increases with r according to equation (2). Comment on their arguments. (2 marks) (b) To study a circular motion, a small rubber bung of mass m is attached to one end of a piece of string passing through a thin glass tube, which has a weight W hanging at its other end. The rubber bung is set into a horizontal circular motion by a student holding the glass tube.

L A

glass tube

paper marker rubber bung W

(i) Draw a diagram to show the forces acting on the rubber bung and explain why the string is not horizontal but dips at a small angle θ. (ii) Show that the weight W equals mω 2L in theory, where ω is the angular speed and L is the length of the string beyond the upper opening of the glass tube. Give TWO reasons to explain why there are discrepancies between the experimental and theoretical results. (iii) Suggest TWO ways to increase the rate of revolution of the rubber bung. (iv) When the rubber bung is at position A, the string suddenly breaks. Describe and explain its subsequent motion. (7 marks) (c) With the aid of a diagram, describe and explain the action of a centrifuge. Give a practical use of a centrifuge. (5 marks) (d) A satellite revolves round the earth whereas an electron revolves round a proton inside a hydrogen atom. State TWO similarities and TWO differences between the two systems. (2 marks)


2. (a) (i) For a sound wave of constant amplitude and frequency travelling through air, sketch a graph to show the time variation of the displacement of the vibrating air particles at a point in the path of the wave. Using the same time axis, sketch also the variation of air pressure with time at the same point. (ii) What is the phase relationship between the displacement and the air pressure in (a)(i)? (2 marks) (b) X loudspeakers

O

Y

Two identical loudspeakers connected to the same signal generator are placed inside a room as shown. All the surfaces of the room are covered with soundabsorbing materials. Point O is equidistant from the loudspeakers are line XOY is parallel to the line joining the loudspeakers. The variation of sound intensity along XOY is shown below: sound intensity

position X

O

Y

(i) Explain why (I) the graph shows alternate maximum and minimum; (II) the sound intensity at a minimum point is non-zero. (ii) State clearly the difference between sound intensity and sound intensity level. Explain why the sound intensity level at O wound decrease by 6 dB if one loudspeaker is turned off. (iii) Explain the change(s), if any, in the variation of sound intensity along XOY if the frequency of the signal generator is increased. (8 marks) (c) With the aid of a diagram, describe an experiment to find the speed of sound in air by using Kundt’s tube together with a loudspeaker. State any precautions which should be taken in the experiment and explain what would be observed. (6 marks)


3. Models are frequently used by physicists to illustrate abstract concepts. This question deals with three of them. (a) (i) In an ideal gas model, gas consists of numerous molecules of negligible volume. These molecules move randomly without intermolecular forces acting between them except during collisions, which are all elastic. Describe qualitatively how this model could provide a microscopic interpretation of the macroscopic quantities such as the pressure and temperature of a gas. (ii) What is an ideal gas from the macroscopic point of view? Under what conditions would a real gas behave like an ideal gas? (4 marks) (b) Briefly describe a simple model for electron conduction in a metal. Explain how this model can account for the heating effect of an electric current in a metal. (6 marks) (c) (i) One of the early models of an atom was introduced by Rutherford. Give a brief description of this atomic model. (ii) How could this model explain the experimental results obtained in the αparticle scattering experiment? (iii) Name ONE phenomenon of an atom that Rutherford’s model failed to account for. (6 marks)

4. Source of energy

Generator

Transformers

Consumers

The above block diagram shows how electric power is supplied to consumers. (a) (i) Name ONE major source of energy that is currently used in electric power stations in Hong Kong. Briefly describe how the energy released from the source can be used to drive a generator in the power station. (ii) Draw a labelled diagram of a simple a.c. generator. State the conditions for the output to be sinusoidal a.c. of frequency 50 Hz. (6 marks) (b) For steady power transmission, show that the power loss in the cables is inversely proportional to the square of the output voltage from the power station. (2 marks) (c) (i) Electric power companies usually use overhead power cables for transmitting electricity over large distance, however the general public


often prefer cables to be underground. Give TWO supporting reasons for each party. (ii) An overhead power cable usually consists of a central core of several steel wires, which is surrounded by many strands of aluminium wire. Give ONE advantage and ONE disadvantage of using aluminium instead of copper. Why is it necessary to include several steel wires in the cable? (6 marks) (d) Low voltage steady d.c. is required for charging a battery inside a Walkman. Draw a circuit diagram to show how the mains supply of 220 V a.c. can be stepped down by a transformer, rectified by a bridge rectifier consisting of four diodes, smoothed by a circuit consisting of two capacitors and an inductor, and finally connected to the battery. (2 marks)

5. (a) Draw a labelled diagram of the basic structure of a cathode-ray tube (CRT) including the electron gun, the deflecting system, the display system and a potentiometer circuit for the E.H.T. supply applied to various parts of the CRT. (Detailed electronic circuits NOT required.) (4 marks) (b) (i) Describe briefly how electrons are produced in the electron gun. (ii) Explain how the sharpness and brightness of the trace on the screen of a CRT can be adjusted. (iii) Explain why the inside of a CRT is coated with graphite and why it is earthed. (6 marks) (c) (i) With the aid of a graph, describe the function of the time base circuit in a CRO. (ii) At the input select of a CRO, the input terminal for a.c., compared with that for d.c. has an extra built-in component. Name that component and state its function. (4 marks) (d) A CRO can be used to measure voltages. Give TWO advantages and TWO disadvantages of using a CRO as a voltmeter as compared with a moving-coil meter. (2 marks)

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1. (a) A man pushes a heavy rock resting on the ground, but it does not move. A student says that this is because the pushing force is balanced by the reaction of this force. Comment, with the aid of a diagram, on whether the student’s argument is correct. (2 marks) (b) Using a spring balance, a small object is found to weigh heavier at the north pole than at the equator. (i) State and explain TWO reasons for this observation. (ii) What would the result be if the object is weighed again at the two places using a beam balance? Explain briefly. (5 marks) (c) Consider the cases in which (i) a man is inside a lift falling freely and (ii) he is inside a space-craft moving in a circular orbit round the earth. Identify THREE similarities between these physical environments. (3 marks) (d) (i) The equation of state and kinetic theory equation of an ideal gas can be 1 written as pV = nRT and pV = Nmc 2 . State the meaning of the symbols 3 excluding pressure p and volume V. (ii) Two identical vessels containing hydrogen and oxygen respectively are at the same temperature and pressure. What can you say about the number of molecules, the average molecular kinetic energy and the mean square speed of the molecules in the two vessels? Explain briefly. (Assume that the gases behave ideally.) (6 marks) 2. (a) Plane monochromatic light waves of wavelength λ are incident normally onto a plane transmission grating of slit separation d to produce an interference pattern. (i) Using the principle of superposition describe briefly how the principal maxima are formed and deduce the formula for the angular positions of the principal maxima. (ii) It is preferable to measure the wavelength of light by using a plane transmission grating rather than using a double slit. Explain briefly. (5 marks) (b) Describe an experiment for observing the absorption spectrum of iodine using a diffraction grating. Describe the spectrum observed and account for it in terms of the quantum nature of light and atomic structure. (8 marks)


(c) Briefly explain the principles involved in identifying the elements present in the atmosphere of the sun through studying the sun’s spectrum. (3 marks)

3. (a) Explain the meaning of the potential difference between two points in an electric field and hence state the meaning of the potential at a point in the field. (3 marks) (b) (i) An isolated spherical conductor is positively charged. Draw carefully on the same diagram (I) the electrostatic lines of force, (II) a series of equipotential surfaces with equal increment in electric potential around the spherical conductor. (ii) With reference to the diagram drawn in (i), (I) explain how the lines of force help in describing an electric field. (II) illustrate the relationship between electric field strength and potential difference. (6 marks) (c) With the aid of a diagram, describe and explain an experiment to investigate the potential around a charged sphere. Briefly describe the experimental results. (7 marks)

4. (a) You are given two bar magnets, a long copper wire and a light beam galvanometer. Describe how you would use the apparatus to investigate qualitatively the factors affecting the e.m.f. induced in a coil by electromagnetic induction. (5 marks) (b) (i) Consider a rectangular coil of N turns rotating uniformly in a uniform magnetic field about an axis perpendicular to the field. Derive an expression for the e.m.f. produced.

uniform magnetic field axis of rotation coil

(ii) With the aid of a labelled diagram, describe the construction of a generator to provide a d.c. to a light bulb using the method in (i) [smoothing is not required]. Show that the current generated is always flowing in one direction through the bulb.


(iii) Explain carefully why a greater driving torque is needed to maintain the coil of the generator rotating at the original speed when an identical light bulb is connected in parallel with the first one. Also explain how this change agrees with the principle of conservation of energy. (11 marks)

5. (a) (i) With the aid of a labelled diagram, explain the working principles of a diffusion cloud chamber. State, with brief explanations, TWO properties of the radiations that could be investigated by the cloud chamber. (ii) The tracks of an α-source are observed in a diffusion cloud chamber in which a trace amount of helium is introduced. Sketch the tracks observed when there is an oblique collision between an α-particle and a helium atom. Show, with mathematical derivation, how the mass of an α-particle can be deduced from these tracks. (The speed of the helium atom before collision is assumed to be negligible.) (10 marks) (b) Explain, through analogous comparison with throwing dice, what is meant by radioactive decay being a ‘random process’. Hence deduce from first principles the exponential law of decay of a radioactive source. (No need to dx describe the dice experiment.) (Given: ∫ = ln x + C ) (6 marks) c

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1. (a) Explain what a simple harmonic motion (s.h.m.) is, and why it is called an isochronous oscillation. (2 marks) (b) A light spring of force constant k is connected to a block of mass m on a frictionless surface inclined at an angle θ to the horizontal. The block is displaced from its equilibrium position O and then released. Suppose at a certain instant the displacement of the block from the equilibrium position is x as shown.

x

O

θ

(i) In terms of the symbols given, express the initial extension e0 of the spring when the block is at its equilibrium position. Show that the period of oscillation of the subsequent motion is independent of the angle of inclination θ. (ii) The motion of the block can be described by the equation x = A cos 2πft where t is the time. State the physical meaning of the quantities A and f. On what factor(s) does each of these quantities depend? (iii) Sketch, for one cycle, three separate graphs to show how the displacement, velocity and acceleration of the block vary with time. Comment on their phase relationship. (No mathematical derivation is required.) (8 marks)


(c)

L

The above figure shows a simple pendulum which consists of a bob suspended by a light, inextensible string of length L from a fixed point. If the bob is slightly displaced to one side and then released, it will perform s.h.m. The setup can be used to measure the acceleration due to gravity g. (i) Which force provides the restoring force for the bob to perform s.h.m.? (ii) Give TWO reasons why a small spherical heavy bob is usually used in the experiment.

L . g Describe briefly how the gravitational acceleration g can be determined from this experiment using a graphical method. State TWO precautions that should be taken in this experiment. (6 marks)

(iii) The period of oscillation of the pendulum is given by T = 2π

2. (a) Explain what is meant by the normal adjustment for an astronomical refracting telescope and why it is used in this way. (2 marks) (b) (i) Draw a diagram to show the passage of three light rays passing through an astronomical refracting telescope from a point on a distant object (not on the axis of the telescope) when it is used with normal adjustment. Mark the foci of the objective lens (F0) and eyepiece (Fe) clearly on your diagram. State the functions of the objective lens and eyepiece. (ii) What is the meaning of the magnifying power of the astronomical refracting telescope with normal adjustment? State the ways of increasing the magnifying power and discuss the limitations on its value. (iii) What is the major disadvantage of the astronomical refracting telescope for viewing objects on the ground? With the help of a suitable diagram, show how this disadvantage can be overcome. (10 marks)


(c) An astronomical refracting telescope may not be able to produce bright images due to reflection from the lens surfaces. Describe and explain a way to reduce the amount of reflected light from the lens surfaces. Why does the objective lens of such a telescope look purple in colour? (No mathematical derivation is required.) (4 marks)

3. (a) (i) A

D

B

C

The figure shows a rectangular metallic loop ABCD being pulled with constant speed out of a magnetic field, which points into the paper. State Lenz’s law and use it together with the idea of changing flux to find the direction of the induced current flowing in the loop. Briefly explain your answer. (ii) What do you understand by the principle of conservation of energy? Referring to the above example, justify whether Lenz’s law satisfies the principle of conservation of energy. (6 marks) (b) (i) Explain why electrical energy is classified as ‘high grade’ while thermal energy is classified as ‘low grade’. (ii) If energy is conserved, why is there an energy crisis? (iii) Discuss THREE advantages and THREE disadvantages of the domestic use of solar energy. (6 marks) (c) (i) Give TWO reasons why the energy in coal or oil is usually converted into electrical energy first instead of being used directly. (ii) Describe the major energy conversions in a coal-fired power station. State a typical conversion efficiency for this kind of power station. (4 marks)


4. (a) (i) Draw a labelled diagram of a simple d.c. motor using permanent magnets. Indicate the direction of rotation of the motor and state the function of the commutator. (ii) Describe and explain THREE modifications for improving the turning effect in practical d.c. motors. (iii) The magnetic fields of some electric motors are provided by electromagnets. Give the advantages of using electromagnets over permanent magnets. (7 marks) (b) coil resistance r M

I S V

The above figure shows a simple motor circuit, in which a constant voltage V is applied to a motor M with coil resistance r while the current flowing is I. (i) Explain why a back e.m.f. (Eb) is generated when the motor rotates and express Eb in terms of I, V and r. Hence explain carefully why the coil of a motor is liable to be damaged when a motor is first switched on or when a running motor is suddenly jammed. (ii) Discuss the variation of current in the above circuit and describe the corresponding changes in the motor’s rotation speed and driving torque when:(I) the switch S is closed and the motor does not carry any mechanical load; (II) a mechanical load is connected to a steadily running motor. (9 marks)


5. (a) Compare how electrons are emitted from metal surfaces in (i) thermionic emission and (ii) photoelectric emission. Suggest TWO reasons why thermionic emission and not photoelectric emission is usually employed in a cathode ray tube for the production of electrons. (3 marks) (b) (i) State TWO experimental facts about photoelectric effect which cannot be explained by the wave theory of light. (ii) Based on the photon theory of light and his photoelectric equation Kmax = hν - φ (Kmax = maximum kinetic energy of emitted photoelectrons), Einstein explained the experimental observation of photoelectric effect described above. (I) State the significance of the terms hν and φ in Einstein’s equation. (II) Explain carefully how Einstein can account for each of the two experimental facts in (b)(i). (6 marks) (c) (i) Explain the origin of the characteristic lines in the hydrogen emission spectrum and the X-ray spectrum. Why do the lines in the X-ray spectrum have much shorter wavelengths? (ii) Explain why there is a continuous spectrum with a minimum wavelength in the X-ray spectrum. (7 marks)

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1. (a) A small ball is projected horizontally with a certain speed from a height of 1 m above a smooth expanse of ground. The ball falls under gravity, hits the ground and bounces up. (i) Assuming that no energy is lost in the process, sketch graphs to show how the vertical component of the velocity and the acceleration of the ball vary with time to the point when the ball bounces up to the original level. Label the axes wherever possible. Describe the force(s) acting on the ball and briefly explain the shape of the graphs. (ii) State the change(s), if any, to the graphs in (a)(i) for the following cases. Briefly explain your answer. (I) A ball of greater mass is used (II) The projection speed is increased (III) Some kinetic energy is lost when the ball hits the ground (iii) Discuss whether the momentum of the ball is conserved when it hits the ground. (12 marks) (b) With the apparatus available in a school laboratory, describe a simple experiment to investigate the dependence of the stopping distance of a vehicle on its initial kinetic energy under the action of a constant resistive force. State and describe how to verify the expected result. State the source(s) of error. (4 marks)

2. (a) (i) With the aid of a diagram, explain how stationary waves are formed. (ii) Explain the following by referring to various phenomena of waves: (I) Radio waves of long wavelengths can propagate long distances. (II) The voice of one of your teachers can be heard and identified before he enters the classroom. (III) Two violin players are playing the same note together for a few seconds and a listener finds that the intensity of the sound seems to vary with time. (IV) A radio receiver seems to work better in some parts of a room than in other parts. (V) Polaroid sunglasses can effectively reduce the glare of the sun reflected from the sea. (10 marks)


(b) You are asked to measure the wavelength of red light using a diffraction grating. With the aid of a diagram, describe how you would carry out the experiment and state any precautions. List the measurements that you would take and the major source of error. (6 marks)

3. (a) A parallel-plate capacitor of capacitance C and a resistor of large resistance R are connected in series with a battery of e.m.f. ε having negligible internal resistance. ε

C

S

R

(i) Sketch graphs to show the time variation of the voltage across the capacitor and the current in the circuit after closing switch S. Briefly explain your answer. (ii) A student uses a voltmeter of resistance R to check the voltage across the capacitor and finds that the reading falls from an initial value ε to a final steady value ε/2. Briefly explain why this is so. (iii) With switch S closed, the plates of the capacitor are pulled apart slightly. Describe and explain the possible change(s) in the charge and the energy stored in the capacitor when the steady state is reached. (8 marks) (b) (i) 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. (ii) (I) State and discuss the significance of the order of magnitude of the internal resistance of a 5 kV E.H.T. (II) A 12 V car battery is designed to deliver a current of a hundred amperes to operate the starting motor. Explain why the headlights would dim when a car is started with the headlights on. (8 marks)


4. (a) (i) With reference to the intermolecular forces, kinetic energy and potential energy of water molecules, describe the changes involved in changing an ice cube at 0 °C to steam at 100 °C. Do you agree that skin burnt by steam at 100 °C is more severe than water at 100 °C? Explain briefly. (ii) Distinguish the terms heat, work and internal energy. Illustrate your answer by describing the energy conversions in a steam turbine. (9 marks) (b) (i) To check for oil leaks in underground pipelines, a radioactive source is put into the pipeline and the radiation is detected on the ground. Discuss what kind of radioactive sources is/are suitable for this purpose. (ii) Radioactive substance Radon-222 Iodine-131

Half-life 3.8 days 8 days

Radiation emitted α γ

(I) Radon gas is usually present in the environment of concrete buildings. Explain why radon is considered to be hazardous to human beings and why opening windows is a way to minimize its hazardous effects. (II) Iodine-131 is used for investigating the absorption of iodine by the thyroid gland. Discuss the suitability of using iodine-131 for this purpose. (7 marks) 5. (a) (i) Using a solenoid connected to an a.c. source of variable frequency, describe a simple experiment to investigate how the induced e.m.f. in a coil depends on the rate of change of magnetic flux linkage through it. List the apparatus used and describe the observation. (ii) State THREE factors that would affect the magnetic flux linkage through a coil. (9 marks) (b) Referring to appropriate physical laws, explain the following: (i) Sparks occur when opening the switch of a circuit with an electromagnet in it. (ii) There is potential difference developed between the wingtips of an aircraft when it is flying horizontally in air. (iii) The pointer of a moving-coil meter stops at the final steady value as soon as it reaches that value and shows no further oscillation. (7 marks) - End of Paper -



1. (a) Explain briefly whether the linear momentum of each of the following underlined objects is conserved: (i) A billiard ball strikes the smooth cushion of a billiard table at an angle and rebounds with the same speed. (ii) A rocket rises vertically upward during launching in the atmosphere near the earth’s surface. (iii) A radioactive nucleus emits an α-particle. (3 marks) (b) A ball of mass m1 moving with velocity u1 undergoes head-on collision with another ball of mass m2 which is initially at rest on a smooth horizontal surface. The collision is perfectly elastic. u1 m1

m2

(i) What is meant by a perfectly elastic collision? Show that the velocity of the ball of mass m1 after collision is given by  m1 − m2  u1   m1 + m2 

(ii) Use the result in (i) to describe examples of collision where (I) m1 is much greater than m2; (II) m1 equal m2; and (III) m1 is much small than m2. Hence explain the implication for the choice of materials used as moderators for neutrons in a nuclear reactor. (7 marks)


(c) The diagram shows a set-up used to measure the speed of a bullet in the laboratory.

θ L

m

v M

The bullet (of mass m, in the form of a small metal ball) is ‘fired’ horizontally towards a block of wood (of mass M, in which a hole has been drilled) suspended from two vertical inextensible strings (each of length L). On striking the block, the bullet is embedded and the block rises by swinging through an angle θ as shown. (i) Suggest a simple method to ‘fire’ the bullet in laboratory. How can we ensure that the bullet will be embedded in the block without rebound? (ii) Show that the speed of the bullets is given by the relation v = m+ M   2 gL (1 − cos θ) where g is the acceleration due to gravity. Indicate   m  clearly the conservation laws applied in deriving the relation. Discuss the account for the discrepancy between the experimental and theoretical values of v. (Neglect the effects of air resistance.) (6 marks)

2. (a) (i) What is Huygens’ principle in describing wave propagation? (ii) Use Huygens’ construction method to explain the refraction of plane waves incident at an angle from air to an optically denser medium. Also derive a relation between the refractive index of the medium and the speed of light in each of the two media. (5 marks) (b) Young’s double slit experiment shows that light propagates as a wave motion. (i) Briefly discuss the precautions of the experiment and the requirements on the set-up in order that best results are obtained when a filament lamp is used. (No need to describe the procedures of the experiment.) (ii) Explain why the two slits cannot be replaced by two light bulbs. (6 marks) (c) The wave theory of light is inadequate for giving a complete explanation of the photoelectric effect, which shows that electromagnetic radiation possesses particle-like properties. (i) What is the photoelectric effect? (ii) Identify and explain TWO experimental results in photoelectric experiments which demonstrate the inadequacy of the wave theory of light.


(5 marks) 3. (a) (i) Give TWO necessary conditions under which the relation Vs : Vp ≈ Ns : Np holds for a transformer. (ii) State and explain TWO designs for a transformer to achieve high efficiency. (iii) The figure below shows a practical transformer with a light bulb connected across the secondary coil.

If an identical light bulb is connected in parallel with the first one, describe what would happen to the secondary current, the secondary voltage, the back e.m.f. in the primary coil and the primary current. (6 marks) (b) Using a simple current balance, describe an experiment to investigate how the magnetic force depends on the length of the current-carrying conductor in the magnetic field. State the precautions for this experiment. (5 marks) (c) (i) Consider a moving-coil meter with a certain current flowing in it. Explain (I) why the magnitude of the deflecting torque due to the current remains the same when the coil rotates, and (II) how equilibrium is achieved at the steady state. (ii) Do you agree that a moving-coil meter would be more accurate when it works in a vacuum? Explain briefly. (iii) Describe and explain what would happen when a d.c. moving-coil meter is used to measure the a.c. mains. (5 marks) 4. (a) (i) Explain the meaning of the marking ‘50 V 470 µF’ on a capacitor. (ii) Explain qualitatively the meaning of self induction by referring to a coil with a decreasing current. (3 marks) (b) A charged ideal capacitor is connected across an ideal inductor. The charges Q d 2Q − 1 oscillating in the circuit satisfies = Q. dt 2 LC (i) Sketch a graph to show the time variation of the energies in the capacitor and the inductor within a period. (ii) Through energy considerations, make an analogy between this capacitorinductor circuit and the mass-spring system that ‘correspond’ to the charge, the


current, the capacitance and the inductance. (Assume no energy loss in both cases.) (iii) Explain why it would be difficult to sustain such an electromagnetic oscillation in practice. With the aid of a graph, describe how the current in the circuit actually varies with time. (10 marks) (c) When each of the components, a resistor, a capacitor and an inductor, is connected to a sinusoidal a.c. supply of variable frequencies, describe how its impedance varies with the applied frequency. Hence explain, with the aid of a circuit diagram, how two of them can be employed to obtain the low frequency component(s) from a multi-frequency a.c. signal. (3 marks)

5. (a) (i) Explain qualitatively, with an example, whether the following laws are consistent with the law of conservation of energy. (I) the first law of thermodynamics (II) Lenz’s law of electromagnetic induction (ii) A student suggests that any allowed physical processes which satisfy the principle of conservation of energy will occur spontaneously. Use an example to show that this is wrong. (5 marks) (b) Energy is released in radioactive decay and nuclear fission. Both processes involve the activities of an atomic nucleus. (i) State THREE differences between these two processes. (ii) Sketch a graph of the binding energy per nucleus against nucleon number and explain why energy can be released in a nuclear fission. Indicate the approximate portion of the graph within which fission may occur. (6 marks) (c) (i) What is meant by a chain reaction? Discuss whether a chain reaction can be sustained in a nuclear reactor if natural uranium is used. (ii) Explain the function of the control rods and the moderator in the steady generation of power inside a nuclear reactor. (5 marks)

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1. (a) (i) What is meant by inertia? Briefly explain its relation to force. (ii) Use an example to illustrate that an object may not necessarily be at rest when the net force acting on it is zero. (3 marks) (b) (i) Give an example in which a body is accelerating but its speed remains unchanged. Briefly explain the motion by using the concepts of force and the change of momentum. (ii) Briefly outline an experiment to show the following relation: force ∝ mass × acceleration Under what condition(s) would the relation become an equation?

(8 marks)

(c) By considering a head-on collision between two moving spheres of different masses, show clearly that the principle of conservation of momentum follows from Newton’s laws of motion. (5 marks)

2. (a) Distinguish between mechanical and electromagnetic waves in terms of their nature and propagation. State the factors governing the speed of mechanical waves in a solid. (3 marks) (b) (i) Describe an experiment, involving a double-slit arrangement, to demonstrate the wave nature of light and to estimate its wavelength. (ii) What further evidence would suggest that a light wave is (I) electromagnetic and (II) transverse? (7 marks) (c) What is the principle of superposition? Use this principle to explain (i) the formation of beats and (ii) the formation of stationary waves. (6 marks)

3. (a) Define electric field intensity and electric potential at a point in an electric field. Derive a relationship between these two quantities. (4 marks) (b) (i) What do you understand by the capacitance of an isolated conductor? Suggest TWO practical applications of capacitors. (ii) With the aid of a diagram, explain how the electric potential and the capacitance of a positive charged, isolated conductor would be affected by a neutral isolated conductor nearby. (6 marks) (c) Describe a method of measuring the capacitance of a parallel-plate air capacitor using a reed switch. Discuss the factors limiting the accuracy of the method. (There is no need to describe the mechanism of the reed switch.) (6 marks)


4. (a) (i) Explain how the SI unit of magnetic field strength, the tesla, is defined. (ii) Explain why two infinitely long straight wires carrying currents in the same direction exert forces on each other. (3 marks) (b) Describe how you would produce a uniform magnetic field using a current-carrying conductor. Briefly describe an experiment using a Hall probe to show that the field is uniform. (6 marks) (c) A metal rod PQ of length l is moved with constant velocity across a uniform magnetic field of flux density B as shown. A potential difference of magnitude Blv is developed across PQ.

P

uniform magnetic field (into paper)

v l

Q

(i) By considering the force(s) acting on an electron in the rod, explain how the potential difference is developed and why it remains constant. (ii) Show that the result is consistent with the law of electromagnetic induction. (iii) What would the situation be if the rod is moved with acceleration? Explain briefly. (7 marks)

5. (a) Give TWO pieces of experimental evidence which support the nuclear model of an atom with energy levels. Briefly explain the implications associated with these pieces of experimental evidence. (4 marks) (b) The energy levels of a hydrogen atom, in eV, are given by En = -13.6/n2

where n = 1, 2, 3, …

(i) With the aid of an energy level diagram, explain the terms ground state and ionization potential as applied to a hydrogen atom. (ii) Describe TWO ways to bring about excitation of a hydrogen atom. How does the concept of energy levels explain the emission line spectrum of hydrogen? (7 marks) (c) Under certain circumstances, electrons can be emitted from substances by photoelectric effect, thermionic emission or radioactivity. For each process,


briefly describe the condition(s) for electron emission and compare the maximum kinetic energy of the emitted electrons. (5 marks)

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1. (a) With the aid of examples, state the magnitude and direction of the resultant force acting on an object that performs (i) projectile motion, (ii) uniform circular motion, and (iii) simple harmonic motion. How does the resultant force bring about the motion in each case? (8 marks) (b) (i) A boy starts to jump vertically from a horizontal ground. Identify all action and reaction pairs involved. Account for his initial acceleration. (ii) Use the concept of action and reaction to explain the launching of rockets. (5 marks) (c) Consider the head-on collision of an α-particle with an isolated gold nucleus that is stationary initially. Explain whether or not the linear momentum of the system is conserved. Describe the energy change during the collision process. (Assume that no excitation of the gold nucleus occurs.) (3 marks)

2. (a) (i) With the aid of a diagram, describe an experiment to demonstrate the interference of a 3 cm microwave using one microwave transmitter. State the appropriate spatial arrangement of the apparatus and briefly explain the experimental result. (ii) State and explain a practical application involving the interference of waves. (6 marks) (b) Large fishing boats are usually equipped with radars and sonars. Describe the working principles of each equipment and state their respective functions. (4 marks) (c) Tidal energy is a renewable energy source. (i) Why is tidal energy classified as ‘renewable’? Describe the principles of a method of harnessing it. (ii) Discuss the factors that need to be considered in harnessing tidal energy near the mouth of a river. (6 marks)

3. (a) (i) Explain the meaning of forced oscillation and resonance. State the phase relationship, in the case of resonance, between the driving force and the displacement of the system that is being driven.


(ii) Sketch graphs to show how the amplitude of forced oscillation depends on the driving frequency when the damping is (I) light and (II) heavy. State and explain TWO considerations in the design of the suspension of a car by referring to the graphs sketched. (8 marks) (b) Describe a practical example of resonance which is (i) acoustic and (ii) electrical. For each example, discuss the factor(s) affecting the resonant frequency. (5 marks) (c) Briefly explain how a laser can produce an intense, monochromatic beam. (There is no need to describe the setting up of an inverted population.) (3 marks)

4. (a) (i) Describe the principles of an experiment that can reveal the sign of the charge carriers in a current-carrying conductor. (ii) Describe and explain, with the aid of graphs, the relation between the current and the applied voltage for (I) a tungsten filament lamp in daily use and (II) a semiconductor diode. Explain in each case any deviation from Ohm’s law. (9 marks) (b) A rectangular coil of N turns, each of area A, is placed with its plane perpendicular to a uniform magnetic field of flux density B as shown. At time t = 0 s, the coil is rotated in a clockwise direction with a uniform angular speed ω. ω

axis of rotation

uniform magnetic field B

coil

(i) Derive an expression for the variation of the induced e.m.f. in the coil with time. Sketch a graph to show its variation within one cycle and indicate when the plane of the coil is parallel to the magnetic field. (ii) In an actual a.c. generator the coil is wound around a soft iron cylinder, which is laminated. State and explain TWO advantages of such a design. (7 marks)


5. (a) Give the meaning of the terms atomic number, mass number and isotopes. (2 marks) (b) You are given some isotopes of a certain element. The isotopes are ionized so that they can carry the same charge Q, and enter a speed selector as shown. Only those isotopes with a definite speed can pass straight through the mutually perpendicular uniform electric and magnetic fields in the speed selector. The whole set-up is in a vacuum environment.

speed selector

a beam of ionized isotopes

(i) Explain how the speed selector works. (ii) Describe and explain how the isotopes can be distinguished experimentally by directing the emerging beam of ionized isotopes into a uniform magnetic field. (7 marks) (c) (i) Give THREE sources of background radiation. (ii) Describe an experiment to show that only α-particles and γ-rays are emitted from a given radioactive source. Account for the experimental result. (7 marks)

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HONG KONG ADVANCED LEVEL EXAMINATION AL PHYSICS 2003 Essay Type Question 1. (a) (i) A block moving with a certain initial speed is acted upon by a constant resultant force F along its direction of motion. Show that the work done by F is equal to the change in kinetic energy of the block. (ii) An electron is projected with an initial velocity v into a region with a uniform magnetic field perpendicular to v. Discuss the work done by the magnetic force acting on the electron and its change in kinetic energy. (Neglect the effects of gravity.) (5 marks) (b) An object is thrown vertically upward from the earth’s surface with a certain initial speed. It rises to a maximum height and then falls back to the starting point. (i) What is the work done by the gravitational force in the process? Explain. (ii) Discuss the effect(s), if any, of the air resistance and upthrust on the final speed of the object when it returns to the starting point. Referring to this example, explain the principle of conservation of mechanical energy and state the necessary condition for it to be valid. (Note: When an object is immersed in a fluid, a constant upward force or upthrust acts on it by the fluid.) (6 marks) (c) Based on the kinetic theory model of an ideal gas, we have the equation 1 pV = Nmc 2 . 3 (i) State TWO assumptions of the kinetic theory model of an ideal gas. Besides pressure p and volume V of an ideal gas, what do the rest of the symbols in the equation represent? (ii) Use the given equation to show how the average kinetic energy of the molecules of an ideal gas is related to its absolute temperature. Explain briefly. (5 marks) 2. (a) State THREE major differences between sound waves and light waves in terms of their physical nature and properties. (3 marks) (b) (i) Describe how Huygens’ construction method can be used to show that (I) light travels in straight lines, and


(II) light refracts when it goes from one medium to another. (ii) Account for the dispersion of white light into different colours by a prism. (Label only the red and violet light rays if you choose to draw a diagram.) (7 marks) (c) Describe an experiment to determine the speed of sound in air. Give the theory and show how the speed of sound is calculated from the measurements. State the source(s) of error of the experiment. (6 marks) 3. (a) (i) A circuit consists of a battery and a resistor connected by conducting wires. Explain why the potential difference across the terminals of the battery is smaller than its e.m.f. (ii) Consider an accumulator being charged by a voltage source, explain the relation between the potential difference across the accumulator and its e.m.f. Briefly describe the energy conversion inside the accumulator during charging. (4 marks) (b) (i) Explain why the order of magnitude of the drift velocity of the free electrons in a circuit is much smaller than their random speeds (~105 ms-1). (ii) Explain why an electric current starts to flow at every point in a circuit almost at the same instant when the switch is closed. (5 marks) (c) (i) Based on the torque acting on a rectangular current-carrying coil in a magnetic field, describe and explain the design feature(s) of a moving-coil galvanometer that give a linear scale. (Mathematical derivation is expected.) (ii) Discuss TWO factors that determine the current sensitivity of the galvanometer. (7 marks) 4. (a) Explain why sparking would occur between the switch contacts if the current in a coil is interrupted when the circuit breaks but not when it is closed. Explain the energy change when the circuit breaks and how sparking can be prevented by adding a capacitor to the circuit. (5 marks) (b) A source of sinusoidal a.c. voltage V = V0 sin (2π f t) is applied across a coil of resistance R and inductance L. (i) Sketch the graphs of current and voltage of the coil against time for 2π f L >> R and explain their phase relationship.


(ii) Illustrate the difference between resistance and reactance by stating their physical meaning. Explain why the size of the current depends on the frequency f of the source. (5 marks) (c) The figure shows the circuit for a power pack. L A

220 V a.c.

D

B C1

C2

R

output

C

(i) Briefly explain how the rectification unit ABCD works. Sketch and explain the output voltage if capacitor C2 and inductor L are absent. (ii) Sketch the voltage across L as well as the output voltage. Account for their shapes by explaining the respective functions of C2 and L. (6 marks) 5. (a) (i) Briefly describe how a hydrogen spectrum can be produced and observed in the laboratory. (ii) Explain why the existence of spectral series of hydrogen supports the theory of discrete energy levels in atoms. (5 marks) (b)

Account for the dark lines in the sun’s spectrum. Explain how the elements in the sun’s atmosphere can be identified by studying these dark lines. (4 marks)

(c)

In an X-ray tube, electrons are accelerated through a large potential difference so that X-rays are produced when the electrons strike a tungsten target. Describe and explain the characteristics of the X-ray spectrum produced. (There is no need to describe the structure of the X-ray tube.) (7 marks)

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HONG KONG ADVANCED LEVEL EXAMINATION AL PHYSICS 2004 Essay Type Question 1. (a) (i) The figure shows a particle moving with uniform speed v in a horizontal circle of radius r. v

A

B r O

With the aid of a vector diagram, find an expression for the change in ρ velocity ∆v as the particle moves from, say, point A to an adjacent point B in time ∆t. Hence, determine the magnitude and direction of its acceleration at point A. (ii) A pendulum bob is attached to a string and made to revolve in a horizontal circle as shown. If the length of the string is L, derive the relation between the period of motion and the angle that the string makes with the vertical. (Neglect air resistance.) (iii) With the aid of a diagram, explain why a person on a bicycle has to lean inwards when riding round a horizontal circular track. (10 marks) (b) Consider the earth as a sphere of uniform density and take RE as the radius of the earth. (i) Explain why, and by how much, an object’s apparent weight indicated by a spring balance at the equator differs from that at the poles. (ii) A simple pendulum and a vertical mass-spring system are set into small oscillations at the equator. Discuss the change in the period of oscillation, if any, for each system if both are set to oscillate at the poles. (Assume that the string of the pendulum is inextensible and the spring is of negligible mass. Neglect air resistance.) (6 marks) 2. (a) Describe how you would demonstrate the existence of electromagnetic radiation just beyond the two ends of the visible spectrum. (5 marks)


(b) What is meant by the diffraction of light? Discuss qualitatively how the size of the obstacle or aperture affects diffraction. Explain whether using red light or blue light can minimize diffraction effects when photographing tiny objects through a microscope. (5 marks) (c) (i) For a parallel beam of light incident normally on a diffraction grating, show, with the aid of a diagram, how the diffracted waves reinforce with each other strongly in certain directions. (ii) State TWO advantages of a diffraction grating compared with a prism for the study of spectra. (6 marks) 3. (a) Explain the meaning of the capacitance of an isolated conductor

(2 marks)

(b) Consider an isolated metal sphere of radius R carrying a charge +Q, (i) sketch the variation of the electric potential due to the charged sphere for all points at a distance r from its centre. Briefly explain the shape of the graph. (ii) derive an expression for the capacitance of the metal sphere. In terms of capacitance, or otherwise, explain the saying that when a charged metal sphere is connected to the earth, it acquires a practical zero of potential. (7 marks) (c) (i) A parallel-plate capacitor of capacitance C is charged by a battery to a potential difference V between its plates. Show, from flfst principles, that 1 the energy stored in it is given by E = CV 2 . With the capacitor 2 disconnected from the battery, how would the energy stored in it be affected when a metal plate is inserted in between? (ii) Suggest TWO uses of capacitors other than energy storage.

(7 marks)


4. (a) Give the meaning of magnetic flux density B in terms of the magnetic force on a current-carrying wire in a uniform magnetic field. (2 marks) (b) (i) What is the relation between magnetic flux Φ and magnetic flux density B? (ii) With the aid of an example, explain the meaning of the equation dΦ ε = −N for electromagnetic induction. dt (iii) N

S

G

Consider a bar magnet being moved towards a coil connected to a galvanometer as shown, illustrate Lenz' s law and how energy is transferred in this process. (7 marks) (c) Referring to a simple d.c. motor, explain the meaning of back e.m.f. An unloaded simple d.c. motor is connected to a constant voltage source. Describe and explain how the back e.m.f. and the current in the coil of the motor change (i) before the motor attains its maximum steady speed, and (ii) when a mechanical load is added to the motor, which then runs steadily to raise the load. (7 marks) 5. (a) Referring to a molecular model of a gas, explain (i) the pressure exerted by the gas on its container (no mathematical derivation is required), and (ii) the meaning of internal energy.

(4 marks)

(b) (i) Identify TWO differences between an ideal gas and a real gas. (ii) Sketch the distribution of molecular speeds at a certain temperature for a fixed mass of an ideal gas. Hence, explain the effect of temperature increase on the proportion of molecules having speeds higher than a certain value.


(iii) For an ideal gas under a certain temperature, find the relation between the root-mean-square speed of the gas molecules and its molecular mass. Hence, determine the ratio of root-mean-square speeds of hydrogen to oxygen, assuming both behave ideally, at room temperature. (Given: relative atomic mass of oxygen is 16.) (6 marks) (c) (i) Despite the fact that energy is conserved, we still have an energy crisis. Explain. (ii) From either economic or environmental point of view, discuss ONE advantage and ONE disadvantage of using the following as an alternative energy source to fossil fuels. (I) nuclear energy (II) hydroelectric power

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(6 marks)

AL Physics 1982-2004 Essay

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