2024 RI Prelim H2 Phy Paper 2

This document consists of 23 printed pages. © Raffles Institution 9749/02 [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2024 Preliminary Examination PHYSICS Higher 2 Paper 2 Structured Questions 9749/02 11 September 2024 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your index number, name and class in the spaces at the top of this page. Write in dark blue or black pen in the spaces provided in this booklet. You may use 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. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use 1 / 8 2 / 9 3 / 5 4 / 8 5 / 10 6 / 8 7 / 10 8 / 22 Deduction Total / 80

2 © Raffles Institution 9749/02 [Turn over Data speed of light in free space c = 81 3.00 10 m s −  permeability of free space 0 = 71 4 10 H m −−  permittivity of free space 0 = 12 1 8.85 10 F m −−  = ( )( ) 91 1 36 10 F m −−  elementary charge e = 19 1.60 10 C −  the Planck constant h = 34 6.63 10 J s −  unified atomic mass constant u = 27 1.66 10 kg −  rest mass of electron me = 31 9.11 10 kg −  rest mass of proton mp = 27 1.67 10 kg −  molar gas constant R = 1 18.31 J K mol − − the Avogadro constant NA = 23 16.02 10 mol − the Boltzmann constant k = 23 11.38 10 J K − − gravitational constant G = 11 226.67 10 N m kg − − acceleration of free fall g = 29.81 m s− Formulae uniformly accelerated motion s = 21 2ut at+ 2v = 2 2u as+ work done on / by a gas W = pV hydrostatic pressure p = ρgh gravitational potential  = Gm r− temperature T/K = / C 273.15T + pressure of an ideal gas p = 21 3 Nm cV mean translational kinetic energy of an ideal gas molecule E = 3 2 kT displacement of particle in s.h.m. x = 0 sinxt  velocity of particle in s.h.m. v = 0 cosvt  22 0xx=  − electric current I = Anvq resistors in series R = 12 RR++ resistors in parallel 1/R = 121 1 RR++ electric potential V = 4 Q r  alternating current/voltage x = 0 sinxt  magnetic flux density due to a long straight wire B = 0 2 d   I magnetic flux density due to a flat circular coil B = 0 2 N r  I magnetic flux density due to a long solenoid B = 0n I radioactive decay x = ( )0 expxt − decay constant  = 12ln2 t

3 © Raffles Institution 9749/02 [Turn over Answer all the questions in the spaces provided. 1 A small ball at the bottom of a frictionless slope is projected up the slope with speed u, as shown in Fig. 1.1. The slope has a height of 4.0 m and makes an angle of 30 to the horizontal ground. Fig. 1.1 (a) In one instance, 17.0 m su −= . (i) Calculate the maximum distance 0s from the bottom of the slope that the ball reaches. 0s = m [2] (ii) As the ball moves up the slope from the bottom, draw on Fig. 1.2 the variation with distance s travelled by the ball from the bottom of the slope of its 1. kinetic energy (label as EK), 2. potential energy (label as EP). Potential energy at the bottom of the slope is zero. [2] Fig. 1.2 s / m energy 0 0 30 4.0 m u ground ball

4 © Raffles Institution 9749/02 [Turn over (b) In another instance, 114.0 m su −= . The ball travels to the top of the slope, leaves the slope and hits the ground. (i) Show that the speed of the ball at the top of the slope is 110.8 m s− . [1] (ii) Calculate the horizontal distance travelled by the ball after it leaves the slope. distance = m [3] [Total: 8]

5 © Raffles Institution 9749/02 [Turn over 2 Two identical balls A and B approach each other along the same straight line on a smooth horizontal surface, as shown in Fig 2.1. Fig. 2.1 At time 0 st = , ball A moves towards ball B with a speed of 14.0 m s− , while ball B moves towards ball A with a speed of 11.0 m s− . Each ball has a mass of 0.50 kg. At time 0.50 st = , the balls undergo a head-on elastic collision and are in contact for a duration of 0.25 s. After the collision, ball A moves with velocity vA and ball B moves with velocity vB. (a) Explain whether both balls could be stationary at the same time during the collision. [2] (b) Show that vB is 14.0 m s− . [2] A B

6 © Raffles Institution 9749/02 [Turn over (c) Calculate the magnitude of the average force on ball A during the collision. Explain your working. force = N [3] (d) Fig. 2.2 shows the variation with time t of the momentum pA of ball A and momentum pB of ball B before the collision. On Fig. 2.2, complete the graphs for pA and pB from 0.50 st = to 1.5 st = . Fig. 2.2 [2] [Total: 9] -3 -2 -1 0 1 2 3 momentum / N s t / s pA pB 0 1.0 0.5 1.5

7 © Raffles Institution 9749/02 [Turn over 3 A uniform circular disc of radius R and weight W is in contact with a smooth horizontal ground and the corner of a box of height 2 R , as shown in Fig. 3.1. A horizontal force F acts at the centre O of the disc to keep the disc in equilibrium. Fig. 3.1 (a) Force F is increased until the disc is just about to rotate about the corner of the box. Use the principle of moments to determine the ratio F W . Explain your working. F W = [3] (b) The box is replaced with one of height R. State and explain how the force F acting at the centre O would need to be changed for the disc to rotate about the corner of the box. [2] [Total: 5] F O R box ground disc

8 © Raffles Institution 9749/02 [Turn over 4 A ball of mass m is attached to one end of a light inextensible string of length L. The other end of the string is attached to a fixed point O. (a) The ball is swung around in a vertical circle, as shown in Fig. 4.1. The speeds of the ball at the top and bottom of the vertical circle are vT and vB respectively. Fig. 4.1 (i) Show that for the ball to just complete the vertical circle, Tv gL= . Explain your working. [2] (ii) Explain why the ratio B T v v must be greater than 1 for the ball to complete the vertical circle. [1] O vT vB L ball string

9 © Raffles Institution 9749/02 [Turn over (iii) A student wishes to swing the ball in a vertical circle such that B T 3v v = . With appropriate calculations, state and explain if this ratio is achievable. [3] (b) The ball is now swung in a horizontal circle around the fixed point O, as shown in Fig. 4.2. When the ball is swinging around with angular velocity  , the string is at an angle  from the vertical and the tension in the string is T. Fig. 4.2 Determine the tension in the string, in terms of T, when the angular velocity of the ball is doubled. tension = [2] [Total: 8] O ball string

10 © Raffles Institution 9749/02 [Turn over 5 (a) The value of the gravitational potential  at a distance x from a point mass M is given by the expression GM x =−