2024 RI Prelim H2 Phy Paper 3 Sect A

This document consists of 20 printed pages. © Raffles Institution 9749/03 [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2024 Preliminary Examination PHYSICS Higher 2 Paper 3 Longer Structured Questions 9749/03 18 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. Section A Answer all questions. Section B Answer one question only and circle the question number on the cover pages. You are advised to spend one and a half hours on Section A and half an hour on Section B. The number of marks is given in brackets [ ] at the end of each question or part question. *This booklet only contains Section A. For Examiner’s Use Section A 1 / 10 2 / 11 3 / 12 4 / 10 5 / 6 6 / 5 7 / 6 Section B (circle 1 question) 8 / 20 9 / 20 Deduction Total / 80

2 © Raffles Institution 9749/03 [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 9749/03 [Turn over Section A Answer all the questions in this section in the spaces provided. 1 (a) State what is meant by the internal energy of an ideal gas. [2] (b) A fixed mass of a n ideal monatomic gas has a volume of 232.0 10 m− at a pressure 51.0 10 Pa . (i) To determine the specific heat capacity of the gas at constant volume, the gas is heated so that its pressure increases to 51.5 10 Pa without any change in volume. 1. Show that the heat supplied to the gas is 1500 J. [1] 2. Determine the increase in temperature of the gas if the average translational kinetic energy of a gas molecule is 216.2 10 J− just before the gas is heated. increase in temperature = °C [3]

4 © Raffles Institution 9749/03 [Turn over (ii) To determine the specific heat capacity of the gas at constant pressure, the gas is heated from its initial state without any change in pressure. State the first law of thermodynamics and use it to explain why the specific heat capacity of the ideal gas determined at constant volume is different to the specific heat capacity when determined at constant pressure. [4] [Total: 10]

5 © Raffles Institution 9749/03 [Turn over 2 A light spring of force constant k hangs vertically from a fixed point. A block of mass m is attached to the free end of the spring, as shown in Fig. 2.1. Fig. 2.1 The block is displaced downwards from its equilibrium position and then released at time 0 st = . (a) The acceleration a of the block is related to its displacement x from the equilibrium position by the equation kax m=− . Explain why the equation leads to the conclusion that the block is performing simple harmonic motion. [2] block spring L block spring L

6 © Raffles Institution 9749/03 [Turn over (b) The variation with time t of the length L of the spring is shown in Fig. 2.2. Fig. 2.2 (i) Determine the maximum speed of the block. speed = 1m s− [2] 12 14 16 18 20 L /

7 © Raffles Institution 9749/03 [Turn over (ii) On Fig. 2.3, show the variation with time t of the velocity v of the block from 0 st = to 1.4 st = . Fig. 2.3 [2] (iii) Determine a value of L at which the potential energy and kinetic energy of the oscillating system are equal. The total potential energy of the oscillating system at equilibrium is taken to be zero. L = cm [2] 0 0.4 0.2 0.6 0.8 1.0 v / 1.4 1.2 t / s

8 © Raffles Institution 9749/03 [Turn over (c) The same block is suspended from two springs as shown in Fig. 2.4. Both springs are identical to that used in Fig. 2.1. Fig. 2.4 The block is pulled down a small distance and released so that it oscillates. By considering the extension at equilibrium of the spring combination in Fig. 2.4, state and explain how the period of these oscillations compares with the period of oscillations in (a). [3] [Total: 11] block

9 © Raffles Institution 9749/03 [Turn over 3 Fig. 3.1 shows, at time 0t , the positions x of the air particles where a progressive sound wave passes through the air towards a reflector. Fig. 3.1 Fig. 3.2 shows, at a later time 1t , the positions x of the same air particles when the reflected sound wave is superposed with the original sound wave to form a stationary wave. Fig. 3.2 (a) Distinguish between progressive and stationary waves in terms of the amplitudes and the phases of oscillations of the particles. amplitudes: phases: [2] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 x / m 0.0 0.2 0.4 0.6 0.8 1.0 1.2 x / m

10 © Raffles Institution 9749/03 [Turn over (b) Use Fig. 3.1 to deduce, with an explanation, (i) the wavelength of the sound wave, wavelength = m [1] (ii) the amplitude of the oscillations of the particles. amplitude = m [2] (c) (i) On Fig. 3.2, indicate all the positions of the displacement nodes (label as N) and displacement antinodes (label as A). [1] (ii) By considering the positions of the particles in Fig. 3.2, draw on Fig. 3.3, the variation with position x of the pressure p of the air when a stationary wave is set up 1. at time 1t (labe