2022 RI Prelims H2 Phy Paper 3 Sect A QP

This document consists of 15 printed pages. © Raffles Institution 9749/03 [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2022 Preliminary Examination PHYSICS Higher 2 Paper 3 Longer Structured Questions 9749/03 21 September 2022 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 page. 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 / 10 3 / 10 4 / 10 5 / 8 6 / 12 Section B (circle 1 question) 7 / 20 8 / 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 41 0 H m   permittivity of free space 0  12 18.85 10 F m    91 13 6 1 0 F m   elementary charge e  191.60 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 2ua s work done on / by a gas W  p V 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 sinx t velocity of particle in s.h.m. v  0 cosvt  22 0x x  electric current I  Anvq resistors in series R  12 RR  resistors in parallel 1/ R  1211 RR  electric potential V  4 Q r alternating current/voltage x  0 sinx t 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) The microscopic potential energy of an ideal gas is taken to be zero. State the assumption of an ideal gas that leads to this result. [1] (b) Fig. 1.1 shows a sealed thermally insulated container with a smooth and light piston that separates two monatomic ideal gases, gas A and gas B. The piston does not allow gas A and gas B to mix but allows heat transfer between them. Fig. 1.1 (i) Initially, 1.8 mol of gas A at temperature 400 K and pressure 53.0 10 Pa occupies a volume of 232.0 10 m while gas B at temperature of 300 K and pressure of 52.0 10 Pa occupies a volume of 233.0 10 m . 1. Show that the amount of gas B is 2.4 mol. [1] 2. Determine the total internal energy of gas A and gas B. total internal ener gy = J [2] gas A gas B insulation piston container

4 © Raffles Institution 9749/03 [Turn over (ii) Due to the difference in pressure of t he gases, the piston moves until both gases achieve thermal equilibrium and the piston is in translational equilibrium. 1. Calculate the final temperature of the gases. Explain your working. temperature = K [2] 2. Use the first law of thermodynamics to explain the change in the temperature of gas A as the system achieves equilibrium. [3] (iii) For the set-up in Fig. 1.1, gas B is now replaced by vacuum. The piston is then removed without any gas escaping or entering the container. It is found that the final temperature of gas A at equilibrium remains at 400 K, which is the same as its initial temperature. Explain why there is no change in the temperature of gas A. [1]

5 © Raffles Institution 9749/03 [Turn over 2 A light spring hangs vertically from a fixed point. A load of mass m is attached to the free end of the spring and slowly lowered until equilibrium is reached as shown in Fig. 2.1. The spring has then stretched elastically by a distance of 0x . Fig. 2.1 (a) (i) Show, for the stretching of the spring, that the decrease in the gravitational potential energy of the mass is twice the increase in the elastic potential energy of the spring. [2] (ii) Account for the difference in the decrease in gravitational potential energy and the increase in elastic potential ener gy. [1] (b) The load on the spring is now made to oscillat e vertically in simple harmonic motion with amplitude 0x . Take the lowest point of the oscillation as the position where the gravitational potential energy of the load is zero. (i) Determine, in terms of m, 0x and the acceleration of free fall g, the elastic potential energy of the spring when the load is at the lowest point of the oscillation. elastic potential energy = [2] spring load of mass m

6 © Raffles Institution 9749/03 [Turn over (ii) Use your answers in (a)(i) and (b)(i) to draw, on the axes of Fig. 2.2, the variation with position of 1. the gravitational potential energy (label this line G.P.E.), 2. the elastic potential energy (label this line E.P.E.), 3. the kinetic energy (label this line K.E.), 4. the total energy (label this line T.E.). Fig. 2.2 [5] lowest point equilibrium position highest point energy

7 © Raffles Institution 9749/03 [Turn over 3 Two identical metal spheres A and B, each with radius R and carrying charge Q , are isolated in space with their centres a distance 2 d apart as shown in Fig 3.1. Assume charges remain uniformly distributed on the surfaces of the spheres. Fig. 3.1 Distance x is measured from the centre of sphere A along the line joining the centres of the two spheres. Point P is the mid-point between the two metal spheres. (a) (i) On Fig. 3.2, sketch the variation with distance x from 0x  to 2xd of the electric potential V between the two spheres. Fig. 3.2 [2] (ii) On Fig. 3.3, sketch the variation with distance x from 0x  to 2xd of the electric field strength E between the two spheres. Fig. 3.3 [2] 0 x V 2dd 0 x E 2dd +Q P +Q 2d sphere A sphere B R R

8 © Raffles Institution 9749/03 [Turn