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1 Answer ALL questions. ii Write your answers in the spaces provided in this Question-Answer Book. You should show all the main steps of your calculations. iii Assume: speed of light in air = 3 x 10 8 m S-l acceleration due to gravity = 10 m S-2 1. A light spring is fixed vertically to a trolley and a light platform is attached to its upper end. A small block of mass m is placed on this horizontal platform. When the system achieves static equilibrium, the spring is compressed by 0.05 m as shown in Figure m uncompressed of the spring position The block is released from the uncompressed position of the spring. The trolley is then given a push so that it moves together with the block at a uniform velocity on a smooth horizontal surface. Neglect air resistance and assume that there is no slipping between the block and the platform.

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3 (iii) Suppose the mass of the block is halved and the force constant of the spring is doubled while its natural length remains unchanged. If the block is again released from the same position and the trolley is given the same uniform velocity as before, find the block's period of oscillation and draw the corresponding stroboscopic photograph in Figure 1.2. Use X to indicate the position of the block. (5 marks) -d Q) S Q),D '0 s:: The trolley is stopped suddenly when the block is just at its highest position. The block slips on -. the platform and then moves off from it. Describe and explain the subsequent motion of the block rn.5 as seen by a stationary observer on the ground. (3 marks) S Q) -B.5 s:: _._ _._--_. rn s:: <r::

4 2. Longitudinal waves can be produced in a metallic slinky spring and the propagation speed of the waves is. I. b JkL 2 h approxunate y given y v = -;;; were k = force constant of the slinky spring L = length of the slinky spring m = mass of the slinky spring A student conducts an experiment to verify this relationship. The spring is stretched to a length of2.2 mas -d shown in Figure 2.2. A battery is connected across the spring and two search coils are placed at A and B '"0 V v "5 which are at a fixed distance 1.0 m apart. The search coils are connected to the respective Y-inputs of a dual,y ti3 8 trace CRO. E. til.5 8.,g Figure " I...j A B search 1.0 m coil D A sharp push is made at the left end of the slinky spring so that a compression pulse travels along the spring. When the compression pulse passes the search coil at A, the following trace is described on the screen of the CRO. I Go on to the next page> Page Total

5 (c) The time interval for the pulse to travel from A to B can be found from the corresponding traces registered by the search coils. The experiment is repeated with the slinky spring stretched to different lengths and the corresponding time intervals found are tabulated below. Complete the table by choosing a suitable physical quantity and plot a straight line graph to -d (l) verify the given relationship. (4 marks) <I:S E (l)..0 Length of the slinky spring, L / m o s:: Time interval for the pulse to travel from A to B, t / s : ;, ; : :,.; ;' ; + ", i,,: -i '; _ ;' +-

6 Calculate the slope of the graph obtained. Hence, estimate a value for the force constant k when the mass of the spring is 0.25 kg. (3 marks) Another student wants to verify whether the propagation speed of the waves is inversely proportional to the square root of the spring's mass. He suggests using slinky springs of. 3 different masses stretched to the same length to repeat the experiment. Explain whether he.5 can verify this relationship by plotting a suitable straight line graph. (2 marks).... $ I Go on to the next page> Page Total

7 3. A student employs the experimental set-up in Figure 3.1 to study a piece of glass of refractive index 1.5 coated with a thin film of refractive index Diagram NOT drawn to scale diffraction grating thin coating, refractive index 1.22 E White light of continuous spectrum from 400 nm to 700 nm is shone normally onto the coated glass. The Cl) light reflected by the coated glass is partly reflected by a 45 partially silvered mirror and incident :: o normally on a diffraction grating with 1000 lines per rom. The colour spectra produced are observed on t:: the screen. en What is the highest order of complete colour spectrum produced? Explain briefly with the aid of.... calculations. (3 marks) S -d Cl) ] ;::

8 (b) In the first-order spectrum produced by the diffraction grating, an intensity minimum is observed at an angular position 33. (ii) Which interface(s) of the coated glass will generate a TC phase change to the reflected light? Explain why there is an intensity minimum in the spectrum. Hence, estimate the minimum possible thickness of the coating on the glass. (5 marks). : en.s S (c) The student suggests that the thickness of the coating could be determined more accurately when the white light source is replaced by a monochromatic laser. Comment on the suggestion.(2 marks) I Go on to the next page> Page Total

9 4. A certain d.c. motor designed to work from a 12 V supply of negligible internal resistance has an armature resistance of 0.25 n. When running freely without any mechanical load, the motor draws a current of 2.0 A from the supply. The magnetic field provided by two curved pole pieces is always parallel to the plane of the armature coil. -..S '" Figure Q).s.S I::: Q).... '"... Q) '" Figure 4.1 shows the side view of the armature coil. At the moment shown, the current is "2 into the paper through arm P while it is out of the paper through arm Q. Indicate the directions of the magnetic forces acting on the arms P and Q. State the sense of rotation 6 of the coil. (2 marks) Q) B' '"... Q) '" The motor is now connected to a mechanical load, and its running speed becomes 80% of the free <C running speed when steady state is reached. Calculate (i) the corresponding back e.m.f., (ii) the current drawn from the supply, (iii) the torque on the armature coil if it is a rectangular coil of 50 turns and area 9.0 x 10-4 m 2 ; and the magnetic field B is 0.1 T.

10 v..... v E _._... _... _... E (d) With the motor connected to the mechanical load, sketch the time variation of the current drawn from the supply when the motor is switched on. Mark the known current values on the vertical axis. (2 marks) current Sources of materials used in this paper will be acknowledged in the Examination Report and Question Papers published by the Hong Kong Examinations and Assessment Authority at a later stage. Answers written in the margins will not be marked.

11 Answer ALL questions. ii Write your answers in the spaces provided in this Question-Answer Book. You should show all the main steps of your calculations. iii Assume: speed of light in air = 3 x 10 8 m S-1 acceleration due to gravity = 10 m S-2 5. In Figure 5.1, a toy is placed on a smooth horizontal surface. It is equipped with a fan powered by a battery. When the fan is switched on, the toy moves to the right and reaches a constant speed eventually. -d <I.l ] E <I.l.D.... s= With the aid of a speed-time o. _. -.._ _ _...._-_._-----.S '" E <I.l -B S s= Q)._ _. _ _._ _.. 'E ;:: '"... <I.l ;:: Cf) s= -<r.: graph, explain the motion of the toy after the fan is switched on. (4 marks) The toy of total mass m is now attached to a fixed point on the ceiling by a light inextensible string of length L. It is set into a uniform horizontal circular motion as shown in Figure 5.2. The string makes an angle e to the vertical when the speed of the toy is v

12 Write down TWO equations of motion of the toy. Hence, show that the angle e satisfies the equation 2 cos 2 e + cos e - 2 = 0 if m = 0.1 kg, L = 0.8 m and v = 2 m S-l and calculate the values of e and T. (5 marks) -d 0..><: a e s:: -. '".5 0/} a e 0..s::....5 s:: 0.1E '" 0 '" s:: «(iii) If the output voltage of the battery inside the toy drops slightly, describe and explain its subsequent motion in terms of v, e and T. (3 marks) I Go on to the next page> Page Total

13 6. The set-up shown in Figure 6.1 is used to study photoelectric effect. Light of a certain frequency is directed towards the photo-sensitive electrode B of a photocell. The potential difference across the electrodes A and B can be varied by adjusting the variable supply. Given Planck constant h = 6.63 X J s Charge of electron e = 1.60 X C --1 electrometer I AI I light photocell IB I variable supply (a) When the voltage VB of the electrode B is zero, the electrometer still detects a current. Explain this phenomenon and state the direction of the current in the photocell. (2 marks) -ci eu a eu.d o t=-._ '".5 a The work function of electrode B IS 2.3 ev. The graph in Figure 6.2 shows the variation of the current f with the voltage VB when the variable supply is adjusted. fila-loa " "

14 What is the maximum kinetic energy, in ev, of the photoelectrons produced? Hence, find the wavelength of the light waves used and name this kind oflight waves. (4 marks).-_..- _ _ _- _ _. _ _._ _..._.. _._.._.. _.._ In Figure 6.2, sketch the current-voltage variation when the experiment is repeated with the light intensity doubled. (2 marks) Referring to the graphs in Figure 6.2, elaborate one observation of the photoelectric effect that cannot be explained by the wave theory. (2 marks) I Go on to the next page> Page Total

15 Figure 7.1 shows an LRC circuit connected to an a.c. source of variable frequency and negligible impedance. The r.m.s. voltage Vs of the source IS 10 V. The resistance of the resistor R is 40 nand L is a pure inductor. r.m.s. voltage across the resistor VRI V /11 R V / / / / / frequency f/ khz With the switch S open and the variable capacitor C set at 1 JlF, the frequency f of the source is varied and the corresponding variation of the r.m.s. voltage V R across the resistor is shown in the above graph. (i) Determine the resonant frequency fa and the maximum value of the r.m.s. current. (3 marks). en.s aa a II).p.5 s::.... II). _ - _ _ _ _ _._ - _ _ _ _._ - _ _ _ _ en s:: < (ii) At resonance, the r.m.s. voltage V L across the inductor is 25 V, which is greater than the r.m.s. voltage of the source. Explain why this is so and find the inductance L. (3 marks)

16 (b) With the switch S still open and the frequency of the source fixed at a certain value ii, the capacitance of the capacitor C is varied so as to study the average power P dissipated in the circuit. " II) ] S II).D os::. Calculate the maximum value of P and state the condition for attaining this value. (3 marks) tn.s.. _ S _--_ e s::. _.._-_. rn l-l II) (c) With the switch S closed and the capacitance fixed, sketch the variation of the Lm.S. voltage across the resistor with the frequency of the source. (2 marks) r.m.s. voltage across the resistor V R I Goon to the next page> Page Total

17 8. Two chambers, X and Y, are separated by a freely movable insulated piston. Each chamber holds 0.15 mole of a monatomic ideal gas. Chamber X is insulated, and chamber Y is maintained at a constant temperature of 20 C. Initially, the temperature in chamber X is 350 C, and the volume of each chamber is 2.0 x 10-3 m 3 (see Figure 8.1). (Given: universal gas constant R = 8.31 J mor1k- 1 ) insulating I wall / "'- / I Chamber X Chamber Y heat 2.0 x 10-3 m 3, 350 C 2.0 X 10-3 m 3,20 C reservoir D C applied force F Figure 8.1 Initial states of the chambers The piston is initially kept at rest by an applied force F as shown. The magnitude of F decreases gradually so that the piston moves to the right very slowly until reaching the final static equilibrium position. The variation in pressure of the chambers during the process is shown in the graph below. The volume of chamber X is taken as the horizontal axis. Pressure II 0 5 Pa (a) Use the graph to find the magnitude of the applied force F required to hold the piston at rest initially. Given that the cross-sectional area of the piston is 4.0 x 10-3 m 2. (2 marks)

18 -ci v S V.D.... o I:: _ s v B.5 c:: v tl 'C I Go on to the next page > Page Total

19 (iii) the work done on the gas in chamber Y, given that the gas in chamber X does a work of 58 J against the applied force F, (2 marks) -d Q) E Q)._ _ _._._---_._._ _ _----_ os:: -..S E s:: _ _ _. _..-_. (iv) the heat absorbed or liberated by the gas in chamber Y. (2 marks) Sources of materials used in this paper will be acknowledged in the Examination Report and Question Papers published by the Hong Kong Examinations and Assessment Authority at a later stage.

20 u 2 2 a=-=oj r r F= Gmtm2 r 2 U=_GMm r r 3 / T 2 = constant flo 1 B=- 2w flon1 B=-- I F = flo I I / 2 2w force per unit length between long parallel straight current-carrying conductors torque on a rectangular current-carrying coil in a uniform magnetic field velocity of transverse wave motion in a stretched string ratio of secondary voltage to primary voltage in a transformer u= velocity oflongitudinal wave motion in a solid f. = -L di dt E =LI2 2 d=ad a 1 X C =- we loglo(-) II =- U v f 1 """2 pv=-nmc 3 E= Q 41r&or 2 V=_Q- 41r& or E=V d electric field strength due to a point charge electric field between parallel plates (numerically) E = 3RT =kt k 2N 2 A E=:/ 1 E =-Fx 2 macroscopic definition of Young modulus C=Q=&oA V d decay of charge with time when a capacitor discharges F=- du dr 1 P+_pu 2 2 +pgh relationship between force and potential energy Q = Qo(l-e- tirc ) rise of charge with time when charging a capacitor!-'u=q+w E = CV2 2 E n = _13.6 ev n2 1 =nauq R= pi A t I In2 "2 k C12. F = BQusinB V = BI nqt force on a moving charge in a magnetic field force on a current-carrying conductor in a magnetic field mu2 = hv-if> 2 m E = mc 2

PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE Form Six Second Term Final Examination ( ) Physics A-Level Paper 1 Question/Answer Book A

05-06/F. 6 Final Exam/AL Physics/Paper 1/P.1 PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE Form Six Second Term Final Examination (2005-2006) A Physics A-Level Paper 1 Question/Answer Book A Time Allowed: