Section A
There are 45 questions in this section. Answer ALL questions. Each question is followed by five suggested answers. Select the best answer in each case. You should spend 1 hour and 45 minutes on this section. Where necessary, take g to be 10 m s-2 and take c to be 3 ´ 108 m s-1.
1.
On the above figure, what is the direction of the total force given by B on A ?
2.
An object is thrown from a cliff with height h at a given angle q to the horizontal with a given initial speed u. It hits the ground at a distance R from the cliff, as shown in the above figure. Which of the following graphs shows the relationship of h and R ?
3.
A particle A of mass mA collides elastically on another particle B of mass mB initially at rest. Particle A leaves at an angle a with the horizontal while B leaves at an angle b with the horizontal. If mA = mB , then
(1) a + b = 90o
(2)
(3) uA2 = vA2 + vB2
A. (3) only
B. (1) and (2) only
C. (1) and (3) only
D. (2) and (3) only
E. (1), (2) and (3)
4.
A rail leans on a smooth wall. The ground is rough enough to prevent the rail from slipping. A ball is released from the top of the rail. Which of the following forces on the rail will decrease as the ball slides down ?
(1) The reaction force by the wall
(2) The vertical component of the reaction force by the ground
(3) The horizontal component of the reaction force by the ground
A. (1) only
B. (3) only
C. (1) and (3) only
D. (2) and (3) only
E. (1), (2) and (3)
5.
A car of 1000 kg is rounding a bended road with an inclination of 45o and radius of curvature 7.63 m at a speed of 20 m s-1. What is the minimum frictional force that the road must give in order to prevent the car from side-slipping ?
A. 1 ´ 104 N
B. 2 ´ 104 N
C. 3 ´ 104 N
D. 4 ´ 104 N
E. 5 ´ 104 N
6.
A trolley of mass 10 kg is projected with an initial speed of 30 m s-1 at the bottom of a smooth circular track of radius 10 m. What is the reaction force given by the track when the trolley reach the topmost point of the track ?
A. 0 N
B. 200 N
C. 400 N
D. 600 N
E. 800 N
7.
A bob of mass 100 g is attached to the lower end of a vertical spring. The spring has an extension of 10 cm when the bob is in equilibrium. The spring is pulled down 3 cm and then released. What is the velocity of the bob when it rises 1 cm ?
A. 0.224 m s-1
B. 0.283 m s-1
C. 0.300 m s-1
D. 2.24 m s-1
E. 2.83 m s-1
8. A particle oscillates under the influence of a driver of frequency fs . In the absence of the driver, the particle performs simple harmonic motion at a frequency f0 . Which of the following correctly describe the phase relationship between the particle and the driver in the forced oscillations ?
(1) When fs < f0 , the driver lags the particle by p/2.
(2) When fs = f0 , the driver is in phase with the particle.
(3) When fs > f0 , the driver is in antiphase with the particle.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1), (2) and (3)
9. A high diver performs somersaults in mid-air and draws his knees close to his chest. Which of the following is/are true ?
(1) Moment of inertia decreases.
(2) Kinetic energy increases.
(3) Angular Momentum increases.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1), (2) and (3)
10. A wire, being stretched by a force F1 , has a length of l1 . If the force is increased gradually from F1 to F2 , causing the length to increase from l1 to l2 , what is the elastic energy stored in the wire during this process ?
A. (F2 – F1)(l2 – l1)
B. (F2 – F1)(l2 – l1)
C. (F1 + F2)(l2 – l1)
D. (F1 + F2)(l2 – l1)
E. (F1 + F2)(l1 + l2)
11.
The above figure shows a Pitot-static tube situated in a moving fluid. If the difference in static tube and total tube levels is 10 cm, what is the speed of the fluid ?
A. 0.5 m s-1
B. 1 m s-1
C. 1.4 m s-1
D. 2 m s-1
E. 4 m s-1
12.
Air is trapped in chamber A which is connected with chamber B. Both chambers have equal volume and have no insulation. Initially, the taps are closed. The gas pressure at chamber A is 3P and chamber B is evacuated. Now tap X is opened and after a while, tap Y is opened. If the atmospheric pressure is P, what is the fraction of gas escaped ?
A. 1/2
B. 1/3
C. 1/4
D. 2/3
E. 3/4
13. A cylinder is fitted with a smooth piston,
(1) it is pushed quickly,
(2) and then the piston is allowed to expand to its original volume.
Which of the following statements is INCORRECT ?
A. In process (1), it is an adiabatic process.
B. There is work done on the gas in process (1).
C. There is no heat exchange with the surrounding in process (1).
D. The work done on the gas in process (1) is equal to the work done by the gas in process (2).
E. There is no change of internal energy of the gas after process (2).
14. Which of the following is/are the differences between real gas and ideal gas ?
(1) Ideal gas obeys Boyles’s law at all pressures and temperature which real gas does not.
(2) Time of collision in ideal gas is negligible which that of real gas is not.
(3) Intermolecular force in ideal gas does not exist which it does exists in real gas.
A. (2) only
B. (3) only
C. (1) and (2) only
D. (1) and (3) only
E. (1), (2) and (3)
15.
An electron is entering a region consists of a uniform electric field and a uniform magnetic field (into the paper) as shown in the diagram. The charged parallel plates are isolated from any power supply. Which of the following statements is/are true ?
(1) There is only one speed of the electron that can make it pass the region undeviated.
(2) If the speed of the electron is increasing, the path of it deviates downwards.
(3) If the separation between the plates is changed, the path of electron still remains unchanged.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1), (2) and (3)
16. Each of the following items involves oscillations :
(1) the tide in Hong Kong harbour
(2) the a.c. mains voltage in Hong Kong
(3) a pendulum 0.4 m long
(4) ultraviolet light
(5) a note on the middle range of the piano
Which of the following places them in the correct order of increasing frequency :
A. (1)(3)(2)(5)(4)
B. (1)(3)(5)(2)(4)
C. (1)(3)(5)(4)(2)
D. (1)(3)(2)(4)(5)
E. (1)(2)(3)(5)(4)
17. A battery-operated buzzer emitting a note of constant frequency is whirled round in a horizontal circle at constant speed on the end of a piece of string. A distant observer hears a note whose pitch varies over a range of 15 Hz. If the rate of rotation is doubled, the pitch varies over a range of x Hz. x is
A. less than 15
B. equal to 15
C. between 15 and 30
D. equal to 30
E. greater than 30
18. A diffraction grating illuminated normally by monochromatic light of wavelength 6.25 ´ 10-7 m gives the second order diffraction image at an angle of 30.00 with the normal to the grating. The number of lines in each mm of the grating is
A. 200
B. 300
C. 400
D. 500
E. 800
19. 2 Hz beats are obtained when a flute and a 512 Hz tuning fork are sounded. When the fork is loaded, the beat frequency becomes 4 Hz. What note(s) could the flute have been playing ?
A. 506 Hz
B. 510 Hz
C. 514 Hz
D. 508 Hz or 516 Hz
E. 510 Hz or 514 Hz
20. A laser beam strikes a grating with horizontal rulings. Which type of pattern results ? In the sketches dark represents light.
21. When unpolarised infra-red travelling in water falls on the surface of a germanium block, at what angle of incidence will the reflected infra-red be plane polarised ? Given that the refractive indexes of water and germanium for infra-red are 1.31 and 4.09 respectively.
A. 17.80
B. 18.70
C. 52.60
D. 72.20
E. 76.30
22. An air-filled resonance tube, open at both ends and resonating to a tuning fork
A. always has a central displacement node.
B. always has a central displacement antinode.
C. always has an odd number of displacement nodes.
D. always has an odd number of displacement antinodes.
E. always has an odd total number of displacement nodes and antinodes.
23. Two waves are superimposed at a point in antiphase. The intensity at that point due to individual waves are 25 W m-2 and 144 W m-2 respectively. What is the resultant intensity at that point ?
A. 13 W m-2
B. 49 W m-2
C. 119 W m-2
D. 169 W m-2
E. 289 W m-2
24. A horizontal straight wire of mass m and length is inclined at angle q to a uniform horizontal magnetic field of flux density B. When current I is passed through the wire it is just self-supporting. What is the value of I ?
A. m ¤ B sinq
B. m ¤ B cosq
C. mg ¤ B sinq
D. mg ¤ B cosq
E. mg ¤ B sinq
25. A uniform copper rod has length , volume V and resistance R. What is the resistance of a uniform copper rod of length 3 and volume V ?
A. R / 3
B. R
C. 3R
D. 9R
E. 27R
26.
The diagram above shows a sinusoidal emf of constant amplitude V and varying angular frequency w applied to a R-C series circuit. Which of the following graphs shows how the amplitude of the current I varies with w ?
27.
A battery of emf E and internal resistance r is connected in series with a resistance R, as shown. With r fixed, the power dissipated in R is maximum for
A. r = 0
B. r = R / 4
C. r = R / 2
D. r = R
E. r = 2R
28. A charge is moved from a point A to another point B. If the work done by electrostatic force is zero, which of the following statement(s) is (are) always true ?
(1) The potentials at A and B are the same
(2) The path of the charge lies on an equipotential surface
(3) The electric field is perpendicular to the path at every point on the path.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1) , (2) and (3)
29.
A capacitor C is charged until it carries a charge Q and then disconnected from the source. If C is now connected to two uncharged identical capacitors as shown, what is the final charge on C ?
A.
B.
C.
D.
E.
30. A charge Q is moving in a circle of radius R with constant speed v. What is the average current set up by such a moving charge ?
A. Q v
B.
C.
D.
E. Q v R
31. The resistivity of a semiconductor decreases rapidly when the temperature increases because
A. semiconductors have large thermal expansitivity.
B. the average kinetic energy of the charge carriers increases rapidly with temperature.
C. the viscous force against the drifting motion of the charge carriers decreases.
D. the positive ions also become mobile.
E. the number of charge carriers increases rapidly with temperature.
32. Which of the following is identical to Tesla, the unit of magnetic flux density ?
(1) N m-1 A-1
(2) Wb m-2
(3) V s m-2
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1) , (2) and (3)
33. A resistor of resistance 120 W is joined in series with a 20 mF capacitor and a sinusoidal a.c. supply of frequency 60 Hz. What is the power factor of the circuit ?
A. 0
B. 0.67
C. 1.0
D. 1.1
E. More data are needed to determine the power factor.
34.