2020 RI Prelims H2 Phy Paper 3 Sect B QP

This document consists of 10 printed pages. © Raffles Institution 9749/03 [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2020 Preliminary Examination PHYSICS Higher 2 Paper 3 Longer Structured Questions 9749/03 23 September 2020 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 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 B. For Examiner’s Use Section B (circle 1 question) 7 / 20 8 / 20 Deduction

2 © Raffles Institution 9749/03 Section B Answer one question from this Section in the spaces provided. 7 A metal cylinder that contains a fixed amount of a monatomic ideal gas is shown in Fig. 7.1. The cylinder is fitted with a piston that moves freely. Fi g. 7.1 Initially, the gas in the cylinder has a volume of 10.0 cm3 and a temperature of 27.0 C. Its initial pressure is the same as the atmospheric pressure of 1.00  105 Pa. (a) (i) Explain what is meant by an ideal gas. [1] (ii) Calculate the number of moles n of gas in the cylinder. n = mol [2] piston metal cylinder ideal gas

3 © Raffles Institution 9749/03 [Turn over (b) The gas in the cylinder undergoes a cycle of changes ABCA, where process AB: the gas is expanded at a constant temperature until its pressure decreases to 0.10  105 Pa. process BC: the gas is heated at a constant volume until it reaches atmospheric pressure again. process CA: the gas is compressed at a constant pressure until it returns to its initial state. Fig. 7.2 shows the p-V curves for two of the three processes. Fig. 7.2 (i) State the first law of thermodynamics, indicating the directions of all energy changes. [1] A C B p / 105 Pa V / cm3

4 © Raffles Institution 9749/03 (ii) With reference to the process AB, 1. state how this process can be achieved in practice, [1] 2. complete Fig. 7.2 by drawing the pV curve as accurately as possible. [2] (iii) With reference to the process BC, show that the heat supplied to the gas is 13.5 J. [2] (iv) With reference to the process CA, 1. by considering the change in internal energy during one complete cycle, state and explain the change in internal energy of the gas during this process, [3] 2. compare the rate at which heat is removed from the gas and the rate at which work is done on the gas. [2]

5 © Raffles Institution 9749/03 [Turn over (c) The product of the pressure p and the volume V of an ideal gas, as derived from the kinetic theory of gases, is given by the equation 21 3pVN m c . (i) State the meaning of each of the symbols N, m and c2. N: m: c2: [2] (ii) State the assumption of the kinetic theory of gases that allows the potential energies associated with the gas particles to be neglected. [1] (iii) Using the given equation in (c), derive an expression for the relationship between the average translational kinetic energy of a gas particle and the thermodynamic temperature T. [1] (iv) Calculate the root-mean-square speed of the gas particles at point B in Fig. 7.2. The mass of one mole of the gas is 14 g. root-mean-square-speed = m s 1 [2]

6 © Raffles Institution 9749/03 8 (a) A rectangular block of length L and cross-sectional area S has an average density . The block is immersed into a mixture of two liquids A and B of densities A and B respectively. The block floats vertically such that the midpoint C of the block is at the interface of the two liquids as shown in Fig. 8.1. Fig. 8.1 (i) Show that the average density  of the block is 11 AB22  . [1] (ii) The upthrust due to liquids A and B are AU and BU , respectively. State and explain whether AU or BU is larger. [2] liquid B of density B liquid A of density A interface between liquids L C cross-sectional area S

7 © Raffles Institution 9749/03 [Turn over (b) Due to some disturbance in the liquids, the block is now rotated slightly about its midpoint C as shown in Fig. 8.2. The block will return to its original vertical orientation. Fig. 8.2 (i) Indicate in Fig. 8.2, the upthrust AU due to liquid A and BU due to liquid B. [2] (ii) Hence by considering the moment of force about C, deduce whether the centre of gravity of the block is above or below C. Explain your reasoning. [2] C

8 © Raffles Institution 9749/03 (c) The block is now given a small displacement x upwards as shown in Fig. 8.2. The block will undergo simple harmonic motion when it is released. Fig. 8.2 (i) Deduce an expression, in terms of S, L, x, A , B and g, for 1. the upthrust in liquid A, [1] 2. the upthrust in liquid B. [1] Cx

9 © Raffles Institution 9749/03 [Turn over (ii) Starting with Newton’s second law, show that the acceleration a of the block when it is released is given by   BA BA 2 gax L      Assume that all viscous forces are negligible and take upwards as positive. [3] (iii) Hence determine the period of oscillation, in terms of g, L, A and B . [2]

10 © Raffles Institution 9749/03 (d) While the block is oscillating, it was found that the speed of the block when the midpoint C crosses the interface between the liquids is 10.40 m s . The length of the block is 0.25 m and the densities of liquids A and B are 3860 kg m and 31300 kg m , respectively. (i) Determine the amplitude 0x of the oscillations. 0x = m [2] (ii) Calculate the period T of oscillations. T = s [1] (iii) Determine the time taken for the midpoint C to travel from  0x x to  1 02x x . time taken = s [3] End of Paper 3 Section B