PHYSICS 9646/01. Paper 1 Multiple Choice 30 September hour 15 minutes

Transcription

1 NANYANG JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION Higher 2 PHYSICS 9646/01 Paper 1 Multiple Choice 30 September 2015 Additional Materials: Multiple Choice Answer Sheet 1 hour 15 minutes READ THESE INSTRUCTIONS FIRST Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name, class and tutor s name on the Answer Sheet in the spaces provided unless this has been done for you. There are forty questions on this paper. Answer all questions. each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet. Read the instructions on the Answer Sheet very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet. This document consists of 18 printed pages. 9646/01/J2PRELIM/15 [Turn over

2 Data 2 speed of light in free space, c = m s -1 permeability of free space, μ o = 4π 10-7 H m -1 permittivity of free space, ε o = F m -1 mulae uniformly accelerated motion, s = ut + ½at 2 v 2 = u 2 + 2as work done on/by a gas, W = pδv hydrostatic pressure, p = ρgh gravitational potential, φ = Gm / r displacement of particle in s.h.m. x = x o sin ωt velocity of particle in s.h.m. v = v o cos ωt mean kinetic energy of a molecule of an ideal gas E = = 2 2 ± ω ( x o x ) 3 2 kt resistors in series, R = R 1 + R 2 + resistors in parallel, 1/R = 1/R 1 + 1/R 2 + electric potential, V = Q / 4πε o r alternating current/voltage, x = x o sin ωt transmission coefficient, T exp(-2kd) where k = 8π 2 m( U E) radioactive decay, x = x o exp (-λt) (1 / (36 π)) 10-9 F m -1 elementary charge, e = C the Planck constant, h = J s unified atomic mass constant, u = kg rest mass of electron, m e = kg rest mass of proton, m p = kg molar gas constant, R = 8.31 J K -1 mol -1 the Avogadro constant, N A = mol -1 the Boltzmann constant, k = J K -1 gravitational constant, G = N m 2 kg -2 acceleration of free fall, g = 9.81 m s -2 h 2 decay constant λ = t /01/J2PRELIM/15

3 3 1 The figure below shows a particle moving with constant speed 10 m s -1 in a horizontal circular path about a point O. What is the change in velocity of the particle in its motion from the point P to the point Q? A B C D 5.0 m s -1 in the direction of PX. 7.3 m s -1 at an angle of 30 to the direction PX. 8.7 m s -1 at an angle of 90 to the direction PX m s -1 at an angle of 120 to the direction PX. 2 The density of a steel ball is determined by measuring its mass and diameter. The mass was measured within 1% and the diameter within 3%. The error in the calculated density of the steel ball is at most A 2% B 4% C 10% D 28% 3 A stone is released from rest at a great height in air and falls owing to gravity. Each of the three graphs below represents the variation with time of one of three variables p, q and r. Which of the following row correctly identifies the three variables p, q and r? p q r A acceleration velocity displacement B acceleration displacement velocity C displacement acceleration velocity D velocity displacement acceleration 9646/01/J2PRELIM/15 [Turn over

4 4 In a tennis match, a ball is hit horizontally with a speed v as shown in the diagram. 4 The bottom of the ball is initially 2.4 m above the ground and at a horizontal distance 12 m from the net. The ball just clears the net, which is 0.90 m high. What is the value of v? (Neglect the effect of air resistance.) A 17 m s -1 B 22 m s -1 C 40 m s -1 D 43 m s -1 5 Two blocks, X and Y of mass m and 3m respectively, are accelerated along a smooth horizontal surface by a force F applied to block Y as shown in the figure below. X F Y The surface between the blocks is rough. If block X does not slide on block Y, what is the frictional force acting on block X? A F 4 B F 3 C F 2 D F 9646/01/J2PRELIM/15

5 5 6 Two spheres, X and Y, are moving towards each other at speeds u 1 and u 2 respectively, and make a head-on elastic collision. After the collision, X and Y move off with speeds v 1 and v 2 respectively, in the directions as shown. before collision X Y u 1 u 2 after collision X Y v 1 v 2 What is the correct expression that equates the relative speed of approach to the relative speed of separation? A u 1 u 2 = v 2 v 1 B u 2 u 1 = v 2 v 1 C u 1 + u 2 = v 1 + v 2 D u 1 + u 2 = v 2 v 1 7 A small raft with a teenager and a bowling ball on it floats in a swimming pool. The water level at the edge of the pool is marked. The teenager drops the bowling ball into the pool. As a result, the level of water in the pool A B C D will rise. will fall. will stay the same. cannot be determined unless the masses of the raft, the teenager and the bowling ball are known. 9646/01/J2PRELIM/15 [Turn over

6 6 8 In order to support a load W, four light hinged rods P, Q, R and S are connected as shown below and mounted in a vertical plane. Which rods are in compression and which are in tension? In compression In tension A P Q, R, S B P, Q R, S C Q, R P, S D R, S P, Q 9 A 50.0 kg block is released from rest at a height 5.00 m above the ground as shown below m It then travels a distance of 10.0 m along a curved slope to the ground. The final speed of the block at the end of the slope is only 4.90 m s -1 because a constant resistive force acts on it during the descent. What is the resistive force acting on the block? A 185 N B 550 N C 2450 N D N 10 A motor operates a machine which conveys 200 balls, each of mass 10.0 g, up a vertical height of 0.50 m every minute, and discharges each ball at a speed of 2.0 m s -1. If 40 % of the work done by the motor is lost, what is the power developed by the motor? A W B 0.38 W C 0.57 W D 23.0 W 9646/01/J2PRELIM/15

7 7 11 A rod is rotating about a pivot as shown. Points P and Q represent the two ends of the rotating rod. Point P moves with a linear speed v P and angular speed ω P, while point Q moves with a linear speed v Q and angular speed ω Q. L 2L P pivot Q Which of the following correctly relates the linear speeds and angular speeds of P and Q? Linear speed Angular speed A v P = v Q ω P = ω Q B v P = v Q 2ω P = ω Q C 2v P = v Q ω P = ω Q D 2v P = v Q 2ω P = ω Q 12 A toy car is released from rest from a height H and allowed to move along a smooth track. It then enters a loop-the-loop of diameter H as shown. toy car Z(highest point) H Y(mid height) X track What is the likely position that the toy car will leave the track? A Between point X and point Y. B At point Y. C Between points Y and Z. D At point Z. 9646/01/J2PRELIM/15 [Turn over

8 8 13 Two stationary particles of mass 32 kg and 100 kg respectively are at a distance 20 m apart. A third particle, lying on the line joining the particles, experiences no resultant gravitational force. What is the distance of this particle from the 32 kg mass? A 4.8 m B 7.2 m C 9.8 m D 11.3m 14 In two widely-separated planetary systems whose suns have masses S 1 and S 2, planet P 1 of mass M 1 and planet P 2 of mass M 2 are observed to have circular orbits of equal radii about S 1 and S 2 respectively. If P 1 completes an orbit in half the time taken by P 2, it may be deduced that A S 1 = 0.25 S 2 only. B S 1 = 0.25 S 2 and M 1 = M 2. C S 1 = 4S 2 only. D S 1 = 4S 2 and M 1 = M Two vessels X and Y, of volume V X and V Y, are kept at temperatures T X and T Y respectively. They are filled with the same ideal gas and connected by a narrow tube. What is the ratio number of molecules in X number of molecules in Y? A TV X TV Y X Y B TV X TV X Y X C TV Y TV Y Y X D TV Y TV X X Y 16 A 2.0 kg chunk of ice at -20 o C is placed in 4.0 kg of water at an initial temperature. What is the initial temperature of the water that will allow all the ice to just melt? Specific heat capacity of water = 4200 J kg -1 K -1 Specific heat capacity of ice = 2100 J kg -1 K -1 Specific latent heat of fusion = J kg -1 A 20 o C B 40 o C C 45 o C D 90 o C 9646/01/J2PRELIM/15

9 9 17 A particle of a mass of 90.0 g undergoes simple harmonic motion. The graph below shows the variation of its kinetic energy E K with time t. E K / J t / ms What is the maximum acceleration of the particle? A m s -2 B m s -2 C 37 m s -2 D 74 m s In microwave ovens, water molecules in food are set into resonance when microwaves of a fixed frequency are incident on them. This causes the molecules to receive energy and hence warms up the food. In order to warm up the food faster, one can A B C D increase the frequency of the incident microwave while keeping its amplitude fixed. increase the frequency and amplitude of the incident microwave. increase the amplitude of the incident microwave while keeping its frequency fixed. keep both frequency and amplitude of the microwave the same as before but increase the frequency of the water molecules. 19 A point source of sound emits energy equally in all directions at a constant rate. A person 8 m from the source listens to the sound. After a short while, the power of the source is halved. How far should the person now be from the source if he wishes to hear the sound with the same loudness as before? A 2 2 m B 4 m C 4 2 m D 8 2 m 20 Which of the following statements describes a situation in which polarisation could not occur? A B C D Light waves pass through a pair of sunglasses. Light waves pass through a liquid crystal display. Microwaves pass through a metal grid. Sound waves pass through a metal grid. 9646/01/J2PRELIM/15 [Turn over

10 10 21 The stationary wave shown below is the result of the superposition of two identical waves travelling in opposite directions. X Y Z Which of the following best states the phase difference between the two waves at points X, Y and Z? X Y Z A π 0 π B π/2 0 π/2 C π/2 π 3π/2 D 0 π 2π 22 The graph below shows the image captured on a screen when monochromatic light from a laser of wavelength 650 nm is projected on a diffraction grating of line density 500 mm 1. intensity displacement / cm y x 0 +x +y If x is 2.5, what is the value of y? A 5.0 B 5.3 C 6.2 D /01/J2PRELIM/15

11 23 Which of the following statements about an electric field is incorrect? 11 A B C D The electric field strength due to a point charge is proportional to 1/r 2 where r is the distance from the charge. Electric field strength is a vector quantity. The electric field strength is zero at all points where the potential is zero. The force acting on an electron, in the electric field between two oppositely charged large parallel plates, is constant. 24 An oil droplet has a charge q and is situated between two parallel horizontal metal plates as shown in the diagram. d -q +V -V The separation of the plates is d. The droplet is observed to be stationary when the upper plate is at potential +V and the lower plate at potential V. this to occur, the weight of the droplet must be equal in magnitude to A Vq d B 2Vq d C Vd q D 2Vd q 25 A slow beam of electrons is accelerated through a uniform electric field, such that the speed of the electron doubles. Current of slow electron beam before acceleration What is the ratio of? Current of accelerated electron beam A 1 B 1/ 2 C 1/2 D 1/(2) /01/J2PRELIM/15 [Turn over

12 12 26 The graph below shows the I-V graph for a conductor X. I / A V / V 6.0 What is the resistance of X when it is connected across a 5.0 V cell? A 0.40 Ω B 0.50 Ω C 2.0 Ω D 2.5 Ω 27 The figure shows the arrangement of four resistors, each with a different resistance. 1 Ω 2 Ω P Q R 8 Ω 4 Ω Which of the following switch settings will produce the greatest current in the circuit? P Q R A Open Open Open B Open Closed Closed C Closed Open Closed D Closed Closed Closed 9646/01/J2PRELIM/15

13 13 28 The figure below shows a circuit containing a cell, an ideal voltmeter, two identical resistors and two switches. V P Q The table below shows the voltmeter readings at different states of the switches. Switch P Open Closed Switch Q Open Open Voltmeter Reading 12.0 V 10.0 V What is the voltmeter reading when both switches are closed? A 8.0 V B 8.6 V C 9.2 V D 10.0 V 9646/01/J2PRELIM/15 [Turn over

14 14 29 The diagram below shows a horizontal plane through which four long straight vertical wires pass. Wires P, Q and R are at three corners of a square and wire S is at the centre. Wire P carries a current of 1 A out of the paper. Wire Q carries 2 A into the paper. Wire R carries 3 A out of the paper. Wire S carries a current out of the paper. Which one of the arrows below shows the direction of the force on wire S? 30 A horseshoe magnet rests on a top-pan balance with a wire situated between the poles of the magnet. With no current in the wire, the reading on the balance is g. With a current of 2.0 A in the wire in the direction XY, the reading on the balance changes to g. What is the reading on the balance, when there is a current of 3.0 A in the wire in the direction YX? A g B g C g D g 9646/01/J2PRELIM/15

15 15 31 The circuit as shown below is set up with the switch closed and a small current is passed through the coil X. The current is slowly increased using the variable resistor. The current reaches a maximum value and is then switched off. The maximum reading on the ammeter occurs when A B C D the current is small, at the beginning. the current is being increased. the current is being switched off. the current in X is zero. 32 A rectangular coil of area A has N turns of wire. The coil is placed in a uniform magnetic field as shown. uniform magnetic field region X X When the coil is rotated at a constant frequency f about axis XX, an alternating e.m.f. of peak value ε o is induced in it. What is the maximum value of the magnetic flux linkage through the coil? A εo 2π f B εo π f C f πf ε π ε o D 2 o 9646/01/J2PRELIM/15 [Turn over

16 16 33 A sinusoidal alternating supply of peak voltage 100 V is connected in series to a diode and a 100 Ω resistor. The diode is ideal with zero forward resistance and an infinite reverse resistance. What is the value of the mean current in the resistor? A B C D less than 0.5 A 0.5 A 0.7 A 1 A 34 A transformer has 1150 turns on the primary coil and 500 turns on the secondary coil. The primary coil draws a current of 0.26 A from a 230 V a.c. supply. The current in the secondary current is 0.50 A. What is the efficiency of the transformer? A 42% B 50% C 84% D 100% 35 An electron of mass m and charge e is accelerated from rest through an electric field of potential difference V. What is the frequency of a photon whose wavelength is equal to the de Broglie wavelength of this electron? (c is the speed of light and h is the Planck constant.) A c 2meV h B c h 2meV C hc ev D ev h 36 The photoelectric work function for sodium is J. Ultraviolet radiation of frequency Hz is directed at a clean sodium surface in a vacuum, causing photoelectric emission. What is the kinetic energy of the fastest electron emitted? A J B J C J D J 37 Which of the following statements about laser is false? A B C D The laser beam is monochromatic because most electrons undergo the same transition. The laser beam is extremely unidirectional. When a laser beam passes through a small aperture, it undergoes diffraction. All photons in the laser cavity are generated by stimulated emission. 9646/01/J2PRELIM/15

17 17 38 The diagram below illustrates how the energy levels of atoms of a substance vary with the inter-atomic separation of the substance. Energy conduction band I valence band II III IV Inter-atomic separation Which of the following statements is incorrect? A B C D I is a metal and IV is a solid state insulator. I is a metal and IV is a gas. II is a semiconductor and IV is a gas. II is a semiconductor and III is a solid state insulator. 39 The isotope Rn decays in a sequence of emissions to form the isotope 82Pb. At each stage of the decay sequence, it emits either an α-particle or a β-particle. What is the number of stages in the decay sequence? A 4 B 8 C 16 D /01/J2PRELIM/15 [Turn over

18 18 40 Alpha, beta and gamma radiations are absorbed to different extents in solids, and behave differently in electric and magnetic fields. The diagrams below illustrate these behaviours. Which three labels on these diagrams refer to the same kind of radiation? A N, Q, X B M, P, Z C L, P, Z D L, P, X 9646/01/J2PRELIM/15

19 H2 Physics Paper 1 Answer Key 1 D 11 C 21 A 31 C 2 C 12 C 22 C 32 A 3 B 13 D 23 C 33 A 4 B 14 C 24 B 34 C 5 A 15 D 25 A 35 B 6 C 16 C 26 D 36 A 7 B 17 D 27 D 37 D 8 D 18 C 28 B 38 A 9 A 19 C 29 B 39 B 10 B 20 D 30 A 40 B

20 NANYANG JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME CLASS TUTOR S NAME PHYSICS 9646/02 Paper 2 Structured Questions 17 September hour 45 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected where appropriate. Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question Total This document consists of 19 printed pages. [Turn over 9646/02/J2PRELIM/15

21 2 Data speed of light in free space, c = m s 1 permeability of free space, μ o = 4π 10 7 H m 1 permittivity of free space, ε o = F m 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, mulae uniformly accelerated motion, s = ut + ½at 2 work done on/by a gas, hydrostatic pressure, v 2 = u 2 + 2as W = pδv p = ρgh gravitational potential, φ = Gm / r displacement of particle in s.h.m. velocity of particle in s.h.m. mean kinetic energy of a molecule of an ideal gas resistors in series, resistors in parallel, electric potential, alternating current/voltage, transmission coefficient, radioactive decay, (1 / (36 π)) 10 9 F m 1 e = C h = J s u = kg m e = kg m p = kg molar gas constant, R = 8.31 J K 1 mol 1 the Avogadro constant, N A = mol 1 the Boltzmann constant, k = J K 1 gravitational constant, G = N m 2 kg 2 acceleration of free fall, g = 9.81 m s 2 x = x o sin ωt v = v o cos ωt = 2 2 ± ω ( x o x ) 3 E = 2 kt R = R 1 + R 2 + 1/R = 1/R 1 + 1/R 2 + V = Q / 4πε o r x = x o sin ωt T exp( 2kd) where k = 8π 2 m( U E) 2 h x = x o exp ( λt) decay constant λ = t /02/J2PRELIM/15

22 1 A speed-time graph for an MRT train travelling between two stations is shown in Fig speed / m s time / s Fig. 1.1 acceleration / m s time / s Fig. 1.2 (a) On Fig. 1.2, draw the corresponding acceleration-time graph. Add numerical values on the acceleration axis. [2] 9646/02/J2PRELIM/15 [Turn over

23 (b) Calculate the distance travelled between the two stations. 4 (c) distance = m [2] On Fig.1.3, sketch a labelled distance-time graph of the train between the two stations. distance / m Fig. 1.3 time / s [3] 9646/02/J2PRELIM/15

24 5 2 Object X, of mass 8.50 kg, is connected to object Y, of mass 5.00 kg, by a light inextensible string as shown in Fig Y X 30 0 Fig. 2.1 Initially, the system is at rest, the spring is at its natural length and there is tension in the string. Assume the incline and pulley are smooth. (a) Explain why X will move up the slope after the system is released from rest. [1] (b) Calculate the speed of X when Y has travelled a distance of 1.50 m. The spring is at its natural length at this moment. speed of X = m s -1 [3] 9646/02/J2PRELIM/15 [Turn over

25 (c) 6 The string is cut and object Y free falls. The speed of Y is 3.00 m s -1 when the spring starts to change its length. The spring has a spring constant of N m -1. Show that the maximum change in length of the spring is m. [2] 3 The variation with displacement of the acceleration of an animal s eardrum is shown in Fig acceleration / m s displacement / cm Fig /02/J2PRELIM/15

26 (a) 7 Explain how Fig. 3.1 shows that the motion of the eardrum is simple harmonic. [2] (b) The period of the oscillation is 2.10 s. Calculate the time taken for the eardrum to travel a distance of 0.50 cm from its maximum displacement. time taken = s [3] (c) The mass of the eardrum is 100 g. Show that the potential energy of the eardrum is J when its displacement is 0.75 cm. [2] 9646/02/J2PRELIM/15 [Turn over

27 8 4 (a) (i) Explain why the gravitational potential at a point in a gravitational field is negative. [1] (ii) The gravitational potential at the surface of Earth is J kg -1, and that at the surface of moon is J kg On Fig. 4.1, sketch a graph which shows the variation of gravitational field strength along a line from the surface of Earth to the surface of Moon. [1] 2. Hence sketch, on Fig. 4.2, a graph which shows the variation of gravitational potential along a line from the surface of Earth to the surface of Moon. [1] Earth Moon Gravitational field strength Distance from surface of Earth Fig. 4.1 Gravitational potential Distance from surface of Earth Fig /02/J2PRELIM/15

28 (b) 9 An isolated spherical planet has a diameter of m. Its mass of kg may be assumed to be a point mass at the centre of the planet. (i) Show that the gravitational field strength at the surface of the planet is 3.7 N kg -1. [1] (ii) A stone of mass 2.4 kg is raised from the surface of the planet through a vertical height of 1800 m. the value of the field strength from (i) to determine the change in gravitational potential energy of the stone. Explain your working. change in gravitational potential energy = J [2] (iii) A rock, initially at rest at infinity, moves towards the planet. At point P, its height above the surface of the planet is 3.5 D, where D is the diameter of the planet, as shown in Fig Fig. 4.3 Calculate the speed of the rock at point P. speed at point P = m s -1 [2] 9646/02/J2PRELIM/15 [Turn over

29 10 5 Electrical wires are often made up of thin copper strands wrapped inside an insulating rubber sheath. Electrical resistivity of copper is Ω m. (a) Calculate the resistance of a thin copper strand of diameter 0.10 mm and length 30 cm. resistance = Ω [2] (b) Calculate the number of such strands in a connecting wire of length 30 cm and resistance 50 mω. number of strands = [2] (c) Two of the wires described in (b) are used to set up the circuit shown in Fig V 24 Ω Fig /02/J2PRELIM/15

30 11 Total Power Loss in Connecting Wires Calculate the ratio of Total Power Supplied by Cell. ratio = [4] (d) Explain why a connecting wire that is made up of thin strands may cause electrical fires if its end is frayed. [2] 6 (a) (i) Explain how band theory predicts that the conductivity of a metal should increase when temperature increases. [2] (ii) Explain why the conductivity of metal actually decreases when temperature increases. [2] 9646/02/J2PRELIM/15 [Turn over

31 12 (b) (i) With reference to a p-type semi-conductor, explain how doping increases the conductivity of the semi-conductor. [2] (ii) Suggest why the resistance of a highly doped semi-conductor will actually increase rather than decrease, when temperature increases. [1] 7 A capillary tube is a tube that is open at both ends and has a very narrow bore. A capillary tube is supported vertically with one end immersed in water. Water rises up the tube due to a phenomenon called capillary action. The water in the bore of the tube forms a column of height h as shown in Fig narrow bore glass wall glass wall h water Fig /02/J2PRELIM/15

32 (a) 13 The height h for a particular capillary tube was measured for different temperatures of the water. The variation with temperature θ of the height h is as shown in Fig h / cm θ / o C Fig. 7.2 (i) Draw the best fit line for the data points on Fig [1] (ii) Explain why the results suggest that the relationship between h and θ is of the form h = h o (1 kθ), where h o and k are constants. [2] 9646/02/J2PRELIM/15 [Turn over

33 (iii) 14 Fig. 7.2 to determine the constants h o and k, with appropriate units. h o = units: [2] k = units: [3] (b) The experiment is repeated using tubes with bores of different radii r but keeping the water temperature constant. Fig 7.3 shows the variation with 1 of the height h for r capillary tubes of different radii r for a water temperature of 20 o C h / m / 10 3 m -1 r Fig /02/J2PRELIM/15

34 15 It is suggested that capillary action is one of the means by which water moves from the roots of a tree to the leaves. (i) Using information from Fig. 7.3, estimate the radius of the bore of the tubes that will enable water to be raised by capillary action from the ground to the top of a tree which has a height of 25 m. State one assumption that was made. Assumption: radius of bore = m [3] [1] (ii) Comment on your answer to (i). [1] (c) Suggest two other factors, apart from temperature and bore radii, which will affect the height h of the column [2] 9646/02/J2PRELIM/15 [Turn over

35 16 8 A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. A varying current in the transformer's primary winding creates a varying magnetic flux in the transformer core and a varying magnetic field impinging on the transformer's secondary winding. Commonly, transformers are used to increase or decrease the voltages of alternating current in electric power applications. A student suggests that if there is a break in the transformer core, the output voltage in the secondary coil will be different from the value when there is no break. To study this effect, a model can be set up using a thin card inserted between two separate iron cores, as shown in Fig Thin card iron cores Fig. 8.1 A coil is wound around one core. A current in the coil may induce an e.m.f. in another coil wound on the other core. The induced e.m.f. V depends on the thickness t of the card. The student suggests that V = V 0 e -αt where V 0 is the induced e.m.f. without card between the cores and α is a constant. Design a laboratory experiment to test the relationship between V and t, and determine the value of α. In your account you should pay particular attention to (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) the analysis of the data, (e) the safety precautions to be taken. 9646/02/J2PRELIM/15

36 Diagram /02/J2PRELIM/15 [Turn over

37 /02/J2PRELIM/15

38 19 [12] 9646/02/J2PRELIM/15 [Turn over

39 NANYANG JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME SOLUTION CLASS TUTOR S NAME PHYSICS 9646/02 Paper 2 Structured Questions 17 September hour 45 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected where appropriate. Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question Total This document consists of 18 printed pages. [Turn over 9646/02/J2PRELIM/15

40 2 Data speed of light in free space, c = m s 1 permeability of free space, μ o = 4π 10 7 H m 1 permittivity of free space, ε o = F m 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, mulae uniformly accelerated motion, s = ut + ½at 2 work done on/by a gas, hydrostatic pressure, v 2 = u 2 + 2as W = pδv p = ρgh gravitational potential, φ = Gm / r displacement of particle in s.h.m. velocity of particle in s.h.m. mean kinetic energy of a molecule of an ideal gas resistors in series, resistors in parallel, electric potential, alternating current/voltage, transmission coefficient, radioactive decay, (1 / (36 π)) 10 9 F m 1 e = C h = J s u = kg m e = kg m p = kg molar gas constant, R = 8.31 J K 1 mol 1 the Avogadro constant, N A = mol 1 the Boltzmann constant, k = J K 1 gravitational constant, G = N m 2 kg 2 acceleration of free fall, g = 9.81 m s 2 x = x o sin ωt v = v o cos ωt = 2 2 ± ω ( x o x ) 3 E = 2 kt R = R 1 + R 2 + 1/R = 1/R 1 + 1/R 2 + V = Q / 4πε o r x = x o sin ωt T exp( 2kd) where k = 8π 2 m( U E) 2 h x = x o exp ( λt) decay constant λ = t /02/J2PRELIM/15

41 1 A speed-time graph for an MRT train travelling between two stations is shown in Fig speed / m s time / s Fig acceleration / m s time / s Fig. 1.2 (a) On Fig. 1.2, draw the corresponding acceleration-time graph. Add numerical values on the acceleration axis. [2] 9646/02/J2PRELIM/15 [Turn over

42 (b) Calculate the distance travelled between the two stations. distance travelled = area under speed-time graph from 0 120s = ½ (20.0)(120+88) 1/2 (20)(5.0) = 2030 = m 4 (c) distance = m [2] On Fig.1.3, sketch a labelled distance-time graph of the train between the two stations. distance / m Fig. 1.3 time / s [3] 9646/02/J2PRELIM/15

43 5 2 Object X, of mass 8.50 kg, is connected to object Y, of mass 5.00 kg, by a light inextensible string as shown in Fig Y X 30 0 Fig. 2.1 Initially, the system is at rest, the spring is at its natural length and there is tension in the string. Assume the incline and pulley are smooth. (a) Explain why X will move up the slope after the system is released from rest. Since the component of the weight of X along the slope (mg sin 30 0 = 42 N) is smaller than the weight of Y (mg = 49 N), X will move up the slope. (b) Calculate the speed of X when Y has travelled a distance of 1.50 m. The spring is at its natural length at this moment. 0 Height gained by X = 1.50sin30 = 0.75 m By conservation of energy, loss in G.P.E of Y = Gain in G.P.E of X + Gain in K.E of X + Gain in K.E of Y = v v ( ) 2 + v = ( ) v = = 1.28 m s 9646/02/J2PRELIM/15 [Turn over

44 (c) 6 The string is cut and object Y free falls. The speed of Y is 3.00 m s -1 when the spring starts to change its length. The spring has a spring constant of N m -1. Show that the maximum change in length of the spring is m. [2] By conservation of energy, loss in G.P.E of Y + Loss in K.E of Y = Gain in E.P.E of spring x = x x 49.05x 22.5 = x = m 3 The variation with displacement of the acceleration of an animal s eardrum is shown in Fig acceleration / m s displacement / cm Fig /02/J2PRELIM/15

45 (a) 7 Explain how Fig. 3.1 shows that the motion of the eardrum is simple harmonic. The graph is a straight line passing through the origin which shows that the acceleration is proportional to the displacement. The straight line has a negative gradient which shows that the acceleration is always directed towards a fixed point / direction of acceleration is always opposite to the direction of displacement. (b) The period of the oscillation is 2.10 s. Calculate the time taken for the eardrum to travel a distance of 0.50 cm from its maximum displacement. When the eardrum travels a distance of 0.50 cm, its displacement will be 1.50 cm. x = x cos( ) 0 ωt 2π 1.50 = 2.00cos( t) 2.10 t = s (c) The mass of the eardrum is 100 g. Show that the potential energy of the eardrum is J when its displacement is 0.75 cm. [2] Total energy of the cymbal = Maximum kinetic energy Potential energy = Total energy - Kinetic energy = mω x0 - mω ( x0 -x ) = mω x = ( ) ( ) -5 = J π = 1 mv = 1 mω x max /02/J2PRELIM/15 [Turn over

46 8 4 (a) (i) Explain why the gravitational potential at a point in a gravitational field is negative. Since the direction of the force exerted by the external agent is opposite to the direction of displacement of the mass when it moves from infinity to a point in the gravitational field, the work done by the external agent is negative. Hence gravitational potential at that point is negative. (ii) The gravitational potential at the surface of Earth is J kg -1, and that at the surface of moon is J kg On Fig. 4.1, sketch a graph which shows the variation of gravitational field strength along a line from the surface of Earth to the surface of Moon. [1] 2. Hence sketch, on Fig. 4.2, a graph which shows the variation of gravitational potential along a line from the surface of Earth to the surface of Moon. [1] Earth Moon Gravitational field strength Distance from surface of Earth Fig. 4.1 Gravitational potential J kg -1 Distance from surface of Earth J kg -1 Fig /02/J2PRELIM/15

47 (b) 9 An isolated spherical planet has a diameter of m. Its mass of kg may be assumed to be a point mass at the centre of the planet. (i) (ii) Show that the gravitational field strength at the surface of the planet is 3.7 N kg -1. [1] GM ( )( ) g = = = 3.69 N kg = 3.7 N kg r ( ) 1 1 A stone of mass 2.4 kg is raised from the surface of the planet through a vertical height of 1800 m. the value of the field strength from (i) to determine the change in gravitational potential energy of the stone. Explain your working. Since the height of 1800 m is much smaller than the radius of the planet, it can be assumed that the stone is moved through 1800 m in a uniform gravitational field. Hence E = mg h = = p 4 2.4(3.7)(1800) J (iii) A rock, initially at rest at infinity, moves towards the planet. At point P, its height above the surface of the planet is 3.5 D, where D is the diameter of the planet, as shown in Fig Fig. 4.3 Calculate the speed of the rock at point P. Assumption: All the loss in gravitational potential energy of the rock is transferred to its kinetic energy. Total final KE + GPE = Total initial KE + GPE 1 2 GMm mv = + 8r GM ( )( ) v = = = m s 6 4r 4( ) /02/J2PRELIM/15 [Turn over

48 10 5 Electrical wires are often made up of thin copper strands wrapped inside an insulating rubber sheath. Electrical resistivity of copper is Ω m. (a) Calculate the resistance of a thin copper strand of diameter 0.10 mm and length 30 cm. R = ρ L / A = / π( ) 2 = 0.65 Ω m 1 resistance = Ω [2] (b) Calculate the number of such strands in a connecting wire of length 30 cm and resistance 50 mω. Strands are in parallel. R = R/N N = R/R = 0.65/0.050 = 13 number of strands = [2] (c) Two of the wires described in (b) are used to set up the circuit shown in Fig V 24 Ω Fig. 5.1 Total Power Loss in Connecting Wires Calculate the ratio of Total Power Supplied by Cell Total resistance = 24 Ω Current in each wire = V / R Total = 2.0 / 24 = A. Total power loss = 2 ( ) = W Total power supplied = I E = = W ratio = [4] Ratio = / = /02/J2PRELIM/15

49 (d) 11 Explain why a connecting wire that is made up of thin strands may cause electrical fires if its end is frayed. Frayed ends: Not all the strands are connected may cause sparking with external surfaces due to potential difference start fires with nearby combustible / flammable materials, or [2] increase in resistance of wire increase in heat generated in wires 6 (a) (i) Explain how band theory predicts that the conductivity of a metal should increase when temperature increases. When temperature increase, more electrons are able to gain sufficient energy to reach the conduction band creating more holes in the valence band increasing the conductivity due to increase in number of charge carriers. [2] (ii) Explain why the conductivity of metal actually decreases when temperature increases. When temperature increase, the lattice vibration will also increase which also decrease the mobility of the charge carriers. When this outweighs the effect of increase in charge carriers, the resistance will increase. [2] 9646/02/J2PRELIM/15 [Turn over

50 12 (b) (i) With reference to a p-type semi-conductor, explain how doping increases the conductivity of the semi-conductor. The acceptor atoms introduce an energy level (called acceptor level) just above the valence band. As the energy gap is smaller now, more electrons are able to enter the acceptor level leaving more holes in the valence band resulting in an increase in the number of holes. This will increase the conductivity for p-type semiconductor. [2] (ii) Suggest why the resistance of a highly doped semi-conductor will actually increase rather than decrease, when temperature increases. A highly doped semiconductor will have relatively large number of charge carrier and it can behave as metals. [1] 7 A capillary tube is a tube that is open at both ends and has a very narrow bore. A capillary tube is supported vertically with one end immersed in water. Water rises up the tube due to a phenomenon called capillary action. The water in the bore of the tube forms a column of height h as shown in Fig narrow bore glass wall glass wall h water Fig /02/J2PRELIM/15

51 (a) 13 The height h for a particular capillary tube was measured for different temperatures of the water. The variation with temperature θ of the height h is as shown in Fig h / cm θ / o C Fig. 7.2 (i) Draw the best fit line for the data points on Fig [1] (ii) Explain why the results suggest that the relationship between h and θ is of the form h = h o (1 kθ), where h o and k are constants. The equation will yield h = h o (h o k) θ, which is in the form of the equation of straight line, y = mx + c. Since the graph of h against θ is a straight line with a negative gradient, with a non-zero y-intercept, the results suggest that the relationship is of the given form. [2] 9646/02/J2PRELIM/15 [Turn over

52 (iii) 14 Fig. 7.2 to determine the constants h o and k, with appropriate units. h o = y-intercept = 16.3 cm (± 0.2 cm) - h o k = gradient of the graph = = (± 0.004) k = = o C -1 h o = units: [2] k = units: [3] (b) The experiment is repeated using tubes with bores of different radii r but keeping the water temperature constant. Fig 7.3 shows the variation with 1 of the height h for r capillary tubes of different radii r for a water temperature of 20 o C h / m Fig r / 10 3 m /02/J2PRELIM/15

53 15 It is suggested that capillary action is one of the means by which water moves from the roots of a tree to the leaves. (i) Using information from Fig. 7.3, estimate the radius of the bore of the tubes that will enable water to be raised by capillary action from the ground to the top of a tree which has a height of 25 m. State one assumption that was made. From the graph, hr = constant. h 1 = r 2 h 2 r r 1 r 1 = m = Assumption: The direct proportion of h with 1 r radius of bore = m [3] holds for values of h up to 25 m. [1] (ii) Comment on your answer to (i). The value of r is very small that it is unlikely that capillary action is the only mechanism that enables water to be raised from the ground to the top of the [1] tree. (c) Suggest two other factors, apart from temperature and bore radii, which will affect the height h of the column. 1. liquid-air surface tension / viscosity of liquid / density of liquid / 2. acceleration due to gravity, g [2] 9646/02/J2PRELIM/15 [Turn over

54 16 8 A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. A varying current in the transformer's primary winding creates a varying magnetic flux in the transformer core and a varying magnetic field impinging on the transformer's secondary winding. Commonly, transformers are used to increase or decrease the voltages of alternating current in electric power applications. A student suggests that if there is a break in the transformer core, the output voltage in the secondary coil will be different from the value when there is no break. To study this effect, a model can be set up using a thin card inserted between two separate iron cores, as shown in Fig Thin card iron cores Fig. 8.1 A coil is wound around one core. A current in the coil may induce an e.m.f. in another coil wound on the other core. The induced e.m.f. V depends on the thickness t of the card. The student suggests that V = V 0 e -αt where V 0 is the induced e.m.f. without card between the cores and α is a constant. Design a laboratory experiment to test the relationship between V and t, and determine the value of α. In your account you should pay particular attention to (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) the analysis of the data, (e) the safety precautions to be taken. 9646/02/J2PRELIM/15

55 Diagram 17 Basic Procedure Vary the thickness t of the thin card (stacking same thicknesses or changing for cards of different thicknesses) B1 Measure V the output of the secondary coil from CRO/voltmeter Diagram of workable procedure (All D marks not awarded if DC source is used) Diagram showing two independent labelled coils wound on iron cores AC power supply connected to one coil Voltmeter / oscilloscope connected in parallel to secondary coil Measurement Measure thickness of card using micrometer / vernier calipers / digital calipers Method to keep current constant rheostat (or variable power supply) and ammeter correctly positioned in primary circuit, so that magnetic flux variation is constant. Analysis (ALL details are required for the mark) Plot a graph of ln V against t or ln V / V 0 against t Relationship is valid if the graph is a straight line with y intercept = ln V 0 α = gradient Additional detail : max 3 large current (in primary coil)/large number of turns on the secondary to achieve measurable V (allow more turns on secondary than primary). Take preliminary readings to ensure that V is measureable. If using CRO for measurement of V, describe how to read V from display Keep frequency of power supply constant or keep the number of turns on each coil constant. laminated cores or use insulated wire for turns. Repeat measurements of t at different positions of card and average. Discuss compression of card / measure t when secured. of dataloggers with appropriate sensors Details describing obtaining V o, must mention gap is closed Other credible details B2 D1 D2 D3 M1 M2 A1 O1 O2 O3 O4 O5 O6 O7 O8 O9 O /02/J2PRELIM/15 [Turn over

56 Safety considerations Precaution linked to hot coil(s) e.g. switch off when not in use / do not touch / wear gloves. 18 S1 Total: /02/J2PRELIM/15

57 H NANYANG JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME CLASS TUTOR S NAME PHYSICS 9646/03 Paper 3 Longer Structured Questions 22 September hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected where appropriate. Section A Answer all questions. Section B Answer any two questions. You are advised to spend about one hour on each section. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. Section A Section B Total This document consists of 23 printed pages. [Turn over 9646/03/J2PRELIM/15

58 2 Data speed of light in free space, c = m s 1 permeability of free space, μ o = 4π 10 7 H m 1 permittivity of free space, ε o = F m 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, mulae uniformly accelerated motion, s = ut + ½at 2 work done on/by a gas, hydrostatic pressure, v 2 = u 2 + 2as W = pδv p = ρgh gravitational potential, φ = Gm / r displacement of particle in s.h.m. velocity of particle in s.h.m. mean kinetic energy of a molecule of an ideal gas resistors in series, resistors in parallel, electric potential, alternating current/voltage, transmission coefficient, radioactive decay, (1 / (36 π)) 10 9 F m 1 e = C h = J s u = kg m e = kg m p = kg molar gas constant, R = 8.31 J K 1 mol 1 the Avogadro constant, N A = mol 1 the Boltzmann constant, k = J K 1 gravitational constant, G = N m 2 kg 2 acceleration of free fall. g = 9.81 m s 2 x = x o sin ωt v = v o cos ωt = 2 2 ± ω ( x o x ) 3 E = 2 kt R = R 1 + R 2 + 1/R = 1/R 1 + 1/R 2 + V = Q / 4πε o r x = x o sin ωt T exp( 2kd) where k = 8π 2 m( U E) 2 h x = x o exp ( λt) decay constant. λ = t /03/J2PRELIM/15

59 3 Section A Answer all the questions in the spaces provided. 1 Fig. 1.1 shows 2 identical magnets moving towards each other on a surface with the same initial speed. Magnets A and B experience the same frictional force which is constant throughout the motion except when they are stationary. Assume friction is negligible when the magnets are stationary and there is negligible air resistance. S N N S magnet A magnet B Fig. 1.1 Fig. 1.2 shows the variation of velocity with time of magnet A during the collision. velocity of magnet A / m s -1 time / 10-2 s Fig /03/J2PRELIM/15 [Turn over

60 (a) Define acceleration. 4 [1] (b) (c) On Fig. 1.2, identify a point where the 2 magnets are closest to each other. Label the point P. [1] Explain why the average gradient of the graph from 0 s to s is greater than the average gradient of the graph from s to s. [3] (d) Using Fig. 1.2 and taking the mass of magnet A to be 0.10 kg, calculate the magnitude of the magnetic force at s. Explain your working. magnetic force = N [2] 9646/03/J2PRELIM/15

61 2 A block of mass m is placed on a horizontal turntable as shown in Fig axis of rotation block turntable Fig. 2.1 The maximum static frictional force F between the table and the block is given by the expression F = 0.80 W where W is the weight of the block. (a) The block is placed at a distance of 0.20 m from the centre of the turntable. Show that the maximum angular speed of the turntable for the block to remain on the turntable is 6.3 rad s -1. [1] (b) (i) The angular speed of the turntable is gradually increased at a constant rate to 6.3 rad s -1. Draw, on Fig. 2.2, an arrow to show the direction of acceleration of the block at the instant when the angular speed is still increasing. [1] block turntable Fig 2.2 (top view) 9646/03/J2PRELIM/15 [Turn over

62 (ii) 6 Suggest why the block will start to slide before it reaches the angular speed 6.3 rad s -1. (iii) Explain why the block will continue to slide while it is still on the turntable. [1] [1] (c) The orientation of the block is then changed such that its centre of gravity is now higher. The angular speed is again increased gradually. Explain why the chance of the block toppling before it slides is now higher. [1] 3 Fig. 3.1 is a full-sized image obtained from a double-slit experiment using a monochromatic light source. Fig. 3.1 (a) Explain the formation of the fringe pattern shown in Fig [2] 9646/03/J2PRELIM/15

63 7 (b) The separation of the double slits is m and the image was captured at a perpendicular distance of 1.6 m from the double slits. Determine the wavelength of the light. wavelength = m [3] (c) State and explain whether similar fringes would be observed if the light from the slits were polarized in perpendicular planes. [2] 4 (a) Define magnetic flux density. [1] (b) e The specific charge of an electron may be measured using the apparatus shown in me Fig (m e is the mass of the electron while e is the elementary charge.) Uniform magnetic field applied in the region from S 1 to A V Fig /03/J2PRELIM/15 [Turn over

64 8 Electrons are emitted from a cathode C and are accelerated by the potential difference V between the cathode and the slit S 1. (i) Show that the speed of the electron at S 1 is 2eV m. [1] e After the electrons pass through the slit S 1, they enter a uniform magnetic field of flux density B as shown in Fig The electrons follow a circular path of radius R, passing through the slits S 2 and S 3, and are collected by the electrode A. The magnitude of the magnetic flux density is adjusted so that the current at the collector is the maximum. (ii) State and explain the direction of the magnetic field. [1] (iii) Determine an expression for e m e in terms of V, B and R. e m = [3] e 9646/03/J2PRELIM/15