Hong Kong Advanced Level Examination

99 AL/Structural Question/P.8

HONG KONG ADVANCED LEVEL EXAMINATION

AL PHYSICS

1999 Structural Question

1. A student tries to measure the density of steel. He puts 20 identical steel ball bearings into a measuring cylinder half filled with water. Figure 1.1 shows the readings of the water level before and after placing the bearings into the cylinder. The ruler used is graduated in mm.

(a) The rise in water level should be recorded as ______± ______(unit: _____ ).

(1 mark)

(b) State and explain one precaution when placing the bearings into the cylinder.

(2 marks)

(c) The internal diameter of the measuring cylinder is found to be 9.40 ± 0.05 mm and the total mass of the ball bearings is 25.00 ± 0.01 g.

(i) Name the instrument used for measuring the internal diameter of the cylinder. (1 mark)

(ii) Find the density of the steel ball bearings. (3 marks)

(iii) Give the percentage uncertainty in your calculated value in (ii). Show your working. (3 marks)

(d) State another method of measuring the density of the ball bearings with a smaller percentage uncertainty. Explain briefly. (3 marks)

2. (a)

Diagram O represents the equilibrium positions of a line of equally spaced selected atoms in a metal. When an ultrasonic wave of a certain frequency travels from left to right in the metal, the positions of the atoms at different times within a period are shown in diagrams P, Q and R.

(i) Which particles in diagram R correspond to rarefactions? (1 mark)

(ii) Find the wavelength, frequency and speed of the ultrasonic wave in the metal. (4 marks)

(b) A student uses the set-up in Figure 2.1 to find the speed of sound in air. The frequency of the signal generator is set at 2 kHz. When the microphone is moved vertically along PQ perpendicular to the bench, a series of alternating maximum and minimum signals are detected. The first maximum signal is found at P while Q corresponds to the fifth maximum. The separation between P and Q is found to be 1.1 m. (Note: The microphone detects the change in pressure caused by the sound waves.)

(i) When the microphone is moved on the bench between point P and the loudspeaker, maximum signals are detected. What can you say about the effect of reflection on a compression of the sound waves incident on the bench? (1 mark)

(ii) Draw on Figure 2.1 the two paths along which sound waves propagate to Q from the loudspeaker. Explain why a series of maximum and minimum signals are detected along PQ. (3 marks)

(iii) Calculate the speed of sound in air. (Hint: Some of the sound waves can be treated as coming from the mirror image of the loudspeaker below the bench.) (4 marks)

3. A proton of mass m and charge q is accelerated from rest through a potential difference V0 and enters perpendicularly through a small hole H on a screen S into a region with a uniform magnetic field B pointing into the paper as shown in Fig. 3.1.

(a) Sketch the path of the proton in Fig. 3.1. Indicate the magnetic force acting on the proton at an arbitrary point on the path. (2 marks)

(b) (i) Derive an expression for the distance d from the hole H to the point where the proton hits the screen. Find this distance for the proton if m = 1.67 ´ 10-27 kg, q = 1.6 ´ 10-19 C, V0 = 1000 V and B = 0.05 T. (4 marks)

(ii) Calculate the time the proton spends in the magnetic field (i.e. the time between leaving H and hitting the screen). (3 marks)

(c) The proton is now replaced by an unknown nucleus X whose charge is double that of a proton. Nucleus X hits the screen at a distance of 0.26 m from H. Compare this with your result in (b)(i), and determine what X is. (3 marks)

4. (a) Figure 4.1 shows an operational amplifier circuit.

A graph of output voltage Vout plotted against input voltage Vin is shown below.

(i) What is the resistance of the resistor Rf? (2 marks)

(ii) With reference to the graph, explain the function of the above circuit.

(3 marks)

(b)

Figure 4.2 shows the circuit of a comparator. The LED lights up when the input voltage Vin is less than 4.5 V. Find the resistance of R. (2 marks)

(c) A stable power supply is essential for the operation of computer parts, which usually work at 5 V d.c. A fluctuation in the supply voltage Vin of more than 10% is certainly not tolerable, so it is therefore important to keep a regular check on it. Figure 4.3 shows a warning device designed for such a purpose.

(i) State the potentials at P and at Q. Briefly explain the operation of the circuit. (3 marks)

(ii) Calculate the resistance of the resistors R1 and R2. (3 marks)

5.   People are often killed in a fire as a result of suffocation. To minimize the loss of lives, smoke detectors can be installed in buildings and a loud sound and a flashing light are triggered when smoke is detected. Figure 5.1 shows a common ionization smoke detector which has a small radioactive source inside. During normal operation, the radioactive source keeps emitting ionizing particles and a certain ionization current is maintained inside the chamber of the detector.

(a) The manufacturer claims that the radioactive source in the smoke detector presents no hazard to health in normal use. Comment on this claim and briefly explain which type of radioactive source should be used in the smoke detector. (3 marks)

(b) When the radioactive source in the detector is placed close to a GM-tube, the count rate measured is 2000 s-1. The average number of ion-pairs produced by each radiation particle is 5 ´ 104 and each ion carries a charge of 1.6 ´ 10-19 C.

(i) Estimate the maximum ionization current in the smoke detector. Why is the ionization current in the smoke detector significantly less than this maximum value? (3 marks)

(ii) The smoke detector should be disposed of when its maximum ionization current drops below 5 ´ 10-12 A. The manufacturer claims that the life of the detector is 10 years. Estimate the half-life of the radioactive source used in the detector. (3 marks)

6. (a) For a source emitting electromagnetic waves of frequency f and moving towards an observer with a velocity v, the frequency of the electromagnetic waves received by the observer is given by

f ’ = (*)

If v < c, show that equation (*) can be approximated to f ’ = .

(2 marks)

(b) An earth satellite in an orbit near the earth’s surface emits a radio signal of frequency 100 MHz. When the satellite passes over a tracking station on the earth’s surface, the station detects beats between the received signal and the station’s own signal of frequency f0. The beat frequency keeps on decreasing from an initial value of 7000 Hz to 2000 Hz within minutes. (The satellite can be considered as moving horizontally with constant velocity during the period of observation).

(i) Explain why the beat frequency changes gradually and not abruptly.

(2 marks)

(ii) Find the speed of the satellite observed from the tracking station.

(3 marks)

(iii) Calculate the frequency f0 of the station’s own signal. (Give your answer up to 6 sig. fig.) (2 marks)

(iv) A student thinks that the calculated value in (ii) is the orbital speed of the satellite. Do you agree with him? Explain briefly. (2 marks)

7. (a) A ball bearing of radius a is released from rest at the edge of the concave side of a cylindrical lens of radius R. The ball bearing rolls without slipping along the curved surface and shows the subsequent oscillatory motion. Neglect the effects of air resistance.

(i) What forces do A, B and C represent? Which force(s) give(s) a torque on the bearing about the contact point P with the lens? (2 marks)

(ii) Explain why the motion of the ball bearing is confined to a vertical plane.

(2 marks)

(iii) For small oscillations, the displacement x of the ball bearing satisfies the equation . It is known that R = 15 cm. Calculate the period of oscillation of the ball bearing. (3 marks)

(iv) The ball bearing is replaced by a hollow sphere having the same mass and same size, and is released from rest at the edge of the concave side of the lens. What is the difference in their speeds when passing the centre of the lens? Briefly explain your answer. (3 marks)

(b) Figure 7.2 shows a slotted weight placed on a horizontal platform. A student attaches the platform to a simple harmonic oscillator which makes it oscillate vertically with amplitude A and variable frequency f. The s.h.m. can be represented by y = A sin (2pft).

(i) Sketch a graph to show the time variation of the force acting on the platform by the slotted weight. (The slotted weight remains in contact with the platform.) (2 marks)

(ii) The frequency of oscillation is gradually increased until it reaches a certain frequency f0 such that the slotted weight starts to lose contact with the platform. Briefly explain the observation and calculate the value of f0 if A = 1.5 cm. (4 marks)

(iii) If the slotted weight is replaced by another one of greater mass, state the change, if any, in the frequency f0 obtained. Explain briefly. (2 marks)

8. (a) Figure 8.1 shows an RC circuit constructed from a capacitor C and a resistor R of resistance 5.5 W.

(i) The frequency of the signal generator is slowly increased from zero. Assume that the r.m.s. output voltage of the signal generator remains constant. Describe the change in the reading of the a.c. ammeter A. Briefly explain your answer. (3 marks)

(ii) The frequency of the signal generator is set at 2 kHz. Figure 8.2 shows the traces of VR and V0 displayed on a CRO.

(I) State the time base used. Use Figure 8.2 to determine the phase relationship between VR and V0. (4 marks)

(II) Find the r.m.s. values of VR and V0 if the voltage gain used is 5 Vcm-1.

(3 marks)

(III) Calculate the capacitance of C. (3 marks)

(b) Figure 8.3 shows a circuit modified from that in Figure 8.1. The inductor L has negligible resistance. Light bulbs X, Y and Z are identical. The frequency of the signal generator is slowly increased from zero. When the frequency reaches 1 kHz, bulbs X and Y glow with equal brightness while bulb Z is dim.

(i) Describe the change in the brightness of the bulbs X and Y before the frequency of the signal generator reaches 1 kHz. Explain briefly.

(3 marks)

(ii) To investigate the voltages across the light bulbs X and Y, the Y-inputs Y1 and Y2 of a dual trace CRO are connected to P and Q respectively. Sketch the traces displayed on the CRO when the frequency of the signal generator is 1 kHz and explain why the bulb Z is dim. (Hint: The sum of currents in X and Y is equal to the current through Z.) (3 marks)

9. In 1989, the spacecraft ‘Voyager 2’ was sent from earth to the Neptunian system. Before this expedition, two satellites of Neptune had been discovered, namely Triton and Nereid. Six more satellites were discovered after this expedition. Their diameters d, periods T and orbital radii about Neptune r are as follows:

Satellite / d/km / T/hr / r/103 km
New:
1989 N1 / 420 / 26.9 / 117.6
1989 N2 / 200 / 13.3 / 73.6
1989 N3 / 140 / 8.0 / 52.5
1989 N4 / 160 / 9.5 / 60.0
1989 N5 / 90 / 7.5 / 50.0
1989 N6 / 50 / 7.1 / 48.2
Previously known :
Triton / 2720 / 140.9 / 354.3
Nereid / 340 / 8640 / 5500

Given : radius of the earth = 6 400 km

(a) (i) Calculate the gravitational potential at the earth’s surface. (2 marks)

(ii) Find the minimum energy supplied to each kilogram of the mass of the spacecraft so as to enable it to escape from the earth’s gravitational pull. Show your working. (2 marks)

(b) Suggest a reason why 1989 N1 was not discovered from earth even though it is bigger than Nereid. (1 mark)

(c) It can be shown that the orbital radius r and period T satisfy the relation where M is the mass of Neptune.

(i) What is the major assumption for the validity of the above relation?

(1 mark)

(ii) Using the information form the newly discovered satellites 1989 N2 to 1989 N6 of Neptume, plot a suitable graph to find the mass of Neptune. Show your working. (6 marks)

(Given : Gravitational constant G = 6.7 ´ 10-11 Nm2kg-2)

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