TJC 2023 H2 Prelim Paper 3

TEMASEK JUNIOR COLLEGE 2023 JC2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME CG PHYSICS 9749/03 Paper 3 Longer Structured Questions 13 September 2023 2 hours Candidates answer on the Question Paper. No additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, CG and subject tutor’s name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB 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 You are advised to spend one and a half hour 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. For Examiner’s Use Section A 1 2 3 4 5 6 Section B 7 8 s.f. Total This document consists of 23 printed pages and 1 blank page.

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 2 Data speed of light in free space c = 3.00 x 108 m s-1 permeability of free space o = 4 x 10-7 H m-1 permittivity of free space o = 8.85 x 10-12 F m-1 or (1/(36)) x 10-9 F m-1 elementary charge e = 1.60 x 10-19 C the Planck constant h = 6.63 x 10-34 Js unified atomic mass constant u = 1.66 x 10-27 kg rest mass of electron me = 9.11 x 10-31 kg rest mass of proton mp = 1.67 x 10-27 kg molar gas constant R = 8.31 J K-1 mol-1 the Avogadro constant NA = 6.02 x 1023 mol-1 the Boltzmann constant k = 1.38 x 10-23 J K-1 gravitational constant G = 6.67 x 10-11 N m2 kg-2 acceleration of free fall g = 9.81 m s-2 Formulae uniformly accelerated motion s = ut + ½ at2 v2 = u2 + 2as work done on/by a gas W = p ΔV hydrostatic pressure p = gh gravitational potential  = –Gm/r temperature T/K = T/oC + 273.15 pressure of an ideal gas p = 3 1 V Nm < c2 > mean translational kinetic energy of an ideal gas molecule E = 2 3 kT displacement of particle in s.h.m. x = xosint velocity of particle in s.h.m. v = vocost = )( 22 xxo − electric current I = Anvq resistors in series R = R1 + R2 + .... resistors in parallel 1/R = 1/R1 + 1/R2 + .... electric potential V = rε4π Q o alternating current/voltage x = xo sint magnetic flux density due to a long straight wire B = 𝜇𝑜𝐼 2𝜋𝑑 magnetic flux density due to a flat circular coil B = 𝜇𝑜𝑁𝐼 2𝑟 magnetic flux density due to a long solenoid B = onI radioactive decay x = x0 exp(−t) decay constant λ = 𝑙𝑛2 𝑡1/2

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 3 [Turn over Section A Answer all the questions in the spaces provided. 1 (a) With reference to electric field lines, explain why, for points outside an isolated charged spherical conductor, the charges on the sphere may be considered to act as a point charge at its centre. [1] (b) Two vertical metal plates in a vacuum have a separation of 4.0 cm. A potential difference of 2.0 × 102 V is applied between the plates. Fig. 1.1 shows a side view of this arrangement. Fig. 1.1 An isolated smoke particle is in the uniform electric field between the plates. The particle has weight 3.9 × 10-15 N and charge -8.0 × 10-19 C. (i) On Fig. 1.1, draw labelled arrows to show the directions of the two forces acting on the smoke particle. [1] (ii) The resultant force acting on the smoke particle is F. Determine 1. the magnitude of F, F = N [3]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 4 2. The angle of F to the horizontal. angle = o [1] (c) (i) The electric field in (b) is switched on at time t = 0 when the particle is at a horizontal displacement s = 2.0 cm from the left -hand plate. At time t = 0 the horizontal velocity of the particle is zero. The particle is then moved by the electric field until it hits a plate at time t = T. On Fig. 1.2, sketch the variation with time t of the horizontal displacement s of the particle from the left-hand plate. Fig. 1.2 [2] (ii) Determine the time T. T = s [2] [Total: 10]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 5 [Turn over 2 (a) State the relationship between gravitational potential  and gravitational field strength g. [1] (b) In a binary star system, star B of mass M and radius R and star A of mass 3M and radius 2R are separated at a distance D between their centres, as shown in Fig. 2.1. Fig. 2.1 Point P is a point along the line between the centres of the two stars, at a variable distance x from the centre star A. The variation with x of the gravitational potential  at point P, for points between the stars is shown in Fig. 2.2. Fig. 2.2 x M

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 6 (i) Deduce whether the gravitational field strength at the surface of star A is greater or less than the gravitational field strength at the surface of star B. Show your workings, if any, in the spaces provided. [2] (ii) Explain the significance of the maximum point M on the graph. [1] (iii) On Fig. 2.3, sketch the variation with x of the gravitational field strength g at point P between x = 2R and x = D – R. No numerical values is required. Fig. 2.3 [2]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 7 [Turn over (c) The stars in (b) are in circular orbits with the same angular speed  and with the centres of both orbits at point C, a distance d from the centre of star A, as shown in Fig. 2.4. Fig. 2.4 (i) Explain why the centripetal force acting on both stars has the same magnitude. [1] (ii) Explain why both stars rotate with the same angular speed . [1] (ii) The separation D of the centres of the stars is 2.8 × 108 km. Determine the distance d. d = km [2] [Total: 10]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 8 3 (a) The internal energy of an ideal gas is dependent on its state, and is given by the sum of the random kinetic energies of all its molecules. (i) Explain why it is important to include the word random in this definition. [1] (ii) Explain why the potential energy of the molecules is not included in this definition. [1] (iii) The pressure p exerted by an ideal gas is given by the equation pc=   21 3 where ρ is the density of the gas. Use this equation to derive an expression for the total internal energy U of n moles of an ideal gas at temperature T. [2] (iv) State two physical conditions under which a real gas will behave approximately as an ideal gas. 1. 2. [2]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 9 [Turn over (b) A heat engine uses 10 moles of an ideal gas as a working substance. Fig. 3.1 shows the changes in pressure and volume of the gas during one cycle ABCA of operation of the engine.