2018 RI H2 Physics Prelims P3 QP

This document consists of 15 printed pages. © Raffles Institution 9749/03 [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2018 Preliminary Examination PHYSICS Higher 2 Paper 3 Longer Structured Questions 9749/03 18 September 2018 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 A. For Examiner’s Use Section A 1 / 10 2 / 12 3 / 12 4 / 13 5 / 13 Section B (circle 1 question) 6 / 20 7 / 20 Deduction Total / 80

2 © Raffles Institution 9749/03 Data speed of light in free space c = 3.00 × 108 m s−1 permeability of free space 0µ = 4π × 10−7 H m−1 permittivity of free space 0ε = 8.85 × 10−12 F m−1 = (1/(36π)) × 10−9 F m−1 elementary charge e = 1.60 × 10−19 C the Planck constant h = 6.63 × 10−34 J s unified atomic mass constant u = 1.66 × 10−27 kg rest mass of electron me = 9.11 × 10−31 kg rest mass of proton mp = 1.67 × 10−27 kg molar gas constant R = 8.31 J K−1 mol−1 the Avogadro constant NA = 6.02 × 1023 mol−1 the Boltzmann constant k = 1.38 × 10−23 J K−1 gravitational constant G = 6.67 × 10−11 N m2 kg−2 acceleration of free fall g = 9.81 m s−2 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 φ = 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 ω velocity of particle in s.h.m. v = 0 cosvt ω 22 0xxω= ±− electric current I = Anvq resistors in series R = 12 ...RR++ resistors in parallel 1/R = 121 1 ...RR++ electric potential V = 4 Q rε0π alternating current/voltage x = 0 sinxt ω magnetic flux density due to a long straight wire B = 0 2 d µ π I magnetic flux density due to a flat circular coil B = 0 2 N r µ I magnetic flux density due to a long solenoid B = 0nµ I radioactive decay x = ( )0 expxt λ− decay constant λ = 1 2 ln2 t

3 © Raffles Institution 9749/03 [Turn over Section A Answer all the questions in this Section in the spaces provided. 1 During a space expedition on the Moon, a table tennis ball is dropped in a large, enclosed container on the surface of the Moon. The container contains air from the Earth. Special arrangements are made to ensure that the pressure of the air is maintained at the Earth’s atmospheric pressure. The variation with time t of the speed v of the table tennis ball is shown in Fig. 1.1. Fig. 1.1 The mass of the table tennis ball is 2.7 g. (a) (i) Use Fig. 1.1 to determine the acceleration of free fall g of the ball on the surface of the Moon. Show your construction on Fig. 1.1. g = m s−2 [2] (ii) If the table tennis ball were dropped outside the container, determine the time taken for it to reach the value of the constant speed in Fig. 1.1. time = s [1] 0.0 1.0 2.0 3.0 4.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 t / s v / m s−1

4 © Raffles Institution 9749/03 (b) The resistive force F acting on the table tennis ball is related to its speed v by the equation F = kv where k is a constant. (i) Calculate the maximum resistive force experienced by the ball as it falls inside the container. maximum resistive force = N [1] (ii) Using your answer in (b)(i), deduce the value of k. k = kg s−1 [1] (iii) Determine the maximum speed of the table tennis ball if this experiment is conducted on the surface of the Earth. maximum speed = m s−1 [2] (iv) Sketch, on Fig. 1.1, a new graph showing the variation with time t of the speed v of the table tennis ball when the experiment is repeated with the following changes made independently: 1. Liquid nitrogen of 1.5 times the mass of the ball is injected into the ball. Label this graph P. 2. The ball is thrown vertically downwards with an initial speed of 4.0 m s –1. Label this graph Q. [3]

5 © Raffles Institution 9749/03 [Turn over 2 (a) (i) Define gravitational field strength. [1] (ii) Hence, state with a reason, if gravitational field strength is a scalar or vector quantity. [1] (iii) State Newton’s law of gravitation and use your definition in (a)(i) to write down an expression for the gravitational field strength g at a distance R from a point mass M. [2] (b) The mass of planet Jupiter is 271.90 10 kg× and its radius is 77.14 10 m× . The radius of Jupiter’s orbit around the Sun is 117.79 10 m× . The mass of the Sun is 301.99 10 kg× . (i) Calculate the ratio gravitational field strength on the surface of Jupiter due to the Sun gravitational field strength on the surface of Jupiter due to the mass of Jupite r . ratio = [2]

6 © Raffles Institution 9749/03 (ii) Hence explain if the gravitational field strength due to the Sun on the surface of Jupiter can be neglected. [1] (c) The Galilean moons are the largest moons of Jupiter which were first discovered by Galileo in January 1610. Some of the data of the 3 Galilean moons closest to Jupiter are given in Fig. 2.1. Name of moon Io Europa Ganymede Average orbital radius / m 84.22 10× 86.71 10× 91.07 10× Fig. 2.1 (i) For moons revolving around a planet in circular orbits, determine that the orbital period T of a moon is given by where R is the radius of the orbit and K is a constant. Explain your working clearly. [3] (ii) Hence, show that the orbital period of Io : Europa : Ganymede is 1 : 2 : 4 approximately. [2] 23T KR=

7 © Raffles Institution 9749/03 [Turn over 3 A test-tube is partially loaded with small ball bearings such that it is able to float upright in water of density ρ as shown in Fig. 3.1. The bottom of the test-tube is a distance H below the water surface. Fig. 3.1 Ignoring its rounded bottom, the test -tube may be regarded as a cylinder of cross sectional area A and mass m. The mass of the ball bearings added is M. (a) Derive an expression that relates H to A, ρ, M and m. [2] (b) The test -tube is displaced vertically by displacement y and then released. Ignoring dissipative forces, (i) write down, in terms of ρ, A, g and y, an expression for the net force acting on the loaded test-tube, [1] (ii) show that the acceleration of the test-tube is given by Agay Mm ρ= − + where g is the acceleration of free fall. [1] water H

8 © Raffles Institution 9749/03 (c) It is given that 331.00 10 kg mρ −= × 426.0 10 mA −= × 0.012 kgM = 0.025 kgm = Show that the period of oscillation of the test-tube is 0.50 s. [3] (d) In practice, it is observed tha