2023 HCI H2 PH Prelim P3A QP

This paper consists of 17 printed pages. HWA CHONG INSTITUTION JC2 Preliminary Examination Higher 2 CANDIDATE NAME CT GROUP 22S CENTRE NUMBER INDEX NUMBER PHYSICS Paper 3 Longer Structured Questions SECTION A BOOKLET Candidates answer on the Question Paper. No Additional Materials are required. 9749/03 18 September 2023 2 hours INSTRUCTIONS TO CANDIDATES Write your Centre number, index number, name and CT class clearly on all 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, paperclips, highlighters, 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. 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. You are reminded of the need for good English and clear presentation in your answers. For Examiner’s Use Section A 1 8 2 8 3 9 4 8 5 8 6 7 7 12 Section B 8 20 9 20 Deductions P3 80

2 © Hwa Chong Institution 9749 / 03 / C2 Preliminary Examination 2023 Data Formulae speed of light in free space, c = 3.00 × 108 m s-1 permeability of free space, μo = 4π × 10-7 H m-1 permittivity of free space, εo = 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 uniformly accelerated motion work done on / by a gas hydrostatic pressure gravitational potential temperature pressure of an ideal gas mean kinetic energy of a molecule of an ideal gas displacement of particle in s.h.m. velocity of particle in s.h.m. electric current resistors in series resistors in parallel electric potential alternating current / voltage magnetic flux density due to a long straight wire magnetic flux density due to a flat circular coil magnetic flux density due to a long solenoid radioactive decay decay constant s = ut + at2 v2 = u2 + 2as W = p ΔV p = ρgh T/K = T/ °C + 273.15 P = x = xo sin ωt v = vo cos ωt = I = Anvq R = R1 + R2 + . . . 1/R = 1/R1 + 1/R2 + . . . x = xo sin ω t B = μonI x = xo exp ( -λt )

3 © Hwa Chong Institution 9749 / 03 / C2 Preliminary Examination 2023 Section A Answer all questions in the spaces provided. 1 (a) Define gravitational potential at a point. ……………………………………………………………………………………………………………. ………………………………………………………………………………………………………… [1] (b) A satellite is orbiting the Earth with an orbital radius of 6610 km at a speed of 7780 m s -1. The satellite is boosted into a higher orbit of radius 6890 km by firing its thrusters. (i) State and explain the effect on the gravitational potential energy of the satellite. …………………………………………………………………………………………………….. ………………………………………………………………………………………………… [1] (ii) Show that the linear speed v of a satellite in a circular orbit of radius R about the centre of the Earth is given by GMv R= where G is the gravitational constant and M is the mass of the Earth. Explain your working. [1] (iii) Show that the speed of the satellite in the new orbit is 7620 m s-1. [1]

4 © Hwa Chong Institution 9749 / 03 / C2 Preliminary Examination 2023 (iv) The satellite has a mass of 120 kg. Using your result in (b), calculate the change in 1. kinetic energy, change in kinetic energy = ……………………. J [2] 2. total energy. change in total energy = …………………..… J [2] [Total: 8]

5 © Hwa Chong Institution 9749 / 03 / C2 Preliminary Examination 2023 2 (a) (i) The pressure p in an ideal gas is given by the expression 21 3 Nmpc V= State the meaning of each of the symbols in the equation. N : …………………………………………………………………………………………………. m : ………………………………………………………………………………………………… V : …………………………………………………………………………………………………. 2c : …………………………………………………………………………………………...… [2] (ii) Using the equation in (i) and the equation of state of an ideal gas, pV = NkT, derive an expression for the relationship between the internal energy of the ideal gas and the thermodynamic temperature T. [2] (b) (i) The gravitational field is relatively weak on the surface of the Moon. The escape speed (i.e. the minimum speed which a body must have in order to escape to an infinite distance) from the Moon is 2.38 km s-1. Argon-40 may be assumed to be an ideal gas. Calculate the temperature of argon-40 gas at which the r.m.s speed of its atoms is equal to the escape speed from the Moon. temperature = ………………….. K [2]

6 © Hwa Chong Institution 9749 / 03 / C2 Preliminary Examination 2023 (ii) An appreciable amount radioactive potassium-40 is discovered below the lunar surface. It is known that potassium-40 decays to form argon-40 gas. With reference to your answer in (b)(i), discuss the likelihood of argon-40 being present in the Moon’s atmosphere. ……………………………………………………………………………………………………... ……………………………………………………………………………………………………... ……………………………………………………………………………………………………... ………………………………………………………………………………………………….. [2] [Total: 8]

7 © Hwa Chong Institution 9749 / 03 / C2 Preliminary Examination 2023 3 A spring hangs vertically from a fixed point. A mass of 1.2 kg is attached to the free end of the spring, as shown in Fig. 3.1. Fig. 3.1 The mass is at the maximum displacement below the equilibrium position at t = 0 s. It undergoes vertical oscillations with frequency 2.5 Hz and amplitude 3.4 cm. Take upwards as positive. (a) The variation with the vertical displacement x of the velocity v of the mass on the spring is shown in Fig. 3.2. On Fig. 3.2. (i) indicate the values where the graph cuts the axes, (ii) mark the starting position at t = 0 s and label this point A. Fig. 3.2 [2] x / m v / m s-1 (0,0)

8 © Hwa Chong Institution 9749 / 03 / C2 Preliminary Examination 2023 (b) For the oscillations of the mass, determine the total energy ET. ET = ………………………. J [2] (c) (i) On Fig. 3.2, mark the position where the potential energy EP is equal to the kinetic energy EK for the first time u