Prelim (H2) P3 2021 QP and Solutions

1 Class Index Number Name 20S ST. ANDREW’S JUNIOR COLLEGE JC 2 2021 Preliminary Examination PHYSICS, Higher 2 9749/03 Paper 3 Longer Structured Questions 16th September 2021 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, index number and Civics Group on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a 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 hours on Section A and half an hour on Section B. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 21 printed pages including this page. SAJC 2021 Preliminary Examination / 9749 [Turn Over For Examiner’s Use Section A 1 / 12 2 / 9 3 / 10 4 / 11 5 / 18 Section B 6 / 20 Total / 80

2 Data speed of light in free space c = 3.00 x 108 m s-1 permeability of free space mo = 4 p x 10-7 H m-1 permittivity of free space eo = 8.85 x 10-12 F m-1 = (1/(36p)) x 10-9 F m-1 elementary charge e = 1.60 x 10-19 C the Planck constant h = 6.63 x 10-34 J s 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 = u t + ½ a t2 v2 = u2 + 2 a s work done on/by a gas W = p DV hydrostatic pressure p = g h gravitational potential f = −Gm r temperature T / K = T / oC + 273.15 pressure of an ideal gas p = 1 3 Nm v ⟨ c2 ⟩ mean translational kinetic energy of an ideal gas molecule E = 3 2 kT displacement of particle in s.h.m. x = xo sin t velocity of particle in s.h.m. v = v0 cos w t v = ± w √ x0 2− x2 electric current I = Anvq resistors in series R = R1 + R2 + ... resistors in parallel 1 / R = 1 / R1 + 1 / R2 + ... electric potential V = Q 4 πε0 r alternating current/voltage x = xo sin  t magnetic flux density due to a long straight wire B = μ0 I 2πd magnetic flux density due to a flat circular coil B = μ0 NI 2r magnetic flux density due to a long solenoid B = μ0 n I radioactive decay x = xo exp (-l t) SAJC 2021 Preliminary Examination / 9749 [Turn Over

3 decay constant  = ln 2 t1/2 SAJC 2021 Preliminary Examination / 9749 [Turn Over

4 Section A Answer all questions in the spaces provided 1 (a) Phobos is one of the two moons orbiting Mars. Fig. 1.1 shows Phobos and Mars. Fig. 1.1 The orbit of Phobos may be assumed to be a circle. The centre of Phobos is at a distance 9380 km from the centre of Mars and it has an orbital speed 2.14 × 103 m s−1. (i) On Fig. 1.1, draw a cross to show the point where the net force acting on a third mass placed at that point is zero. [1] (ii) Calculate the mass M of Mars. M = ………………………….. kg [4] SAJC 2021 Preliminary Examination / 9749 [Turn Over

5 (b) The Earth and Mars move in elliptical orbits around the Sun. In July 2018, the closest distance between the centre of Mars and the centre of Earth will be 5.8 × 1010 m. Fig. 1.2 shows the variation of the resultant gravitational field strength g between the two planets with distance r from the centre of the Earth. Fig. 1.2 (i) Explain briefly the overall shape of the graph in Fig. 1.2. .…………….…………………….…………………….…………………….……………. .…………….…………………….…………………….…………………….……………. .…………….…………………….…………………….…………………….……………. .…………….…………………….…………………….…………………….………... [2] (ii) Determine the ratio mass of Earth mass of Mars . mass of Earth mass of Mars = ………………………….. [2] SAJC 2021 Preliminary Examination / 9749 [Turn Over

6 (iii) After successfully collected some geological samples on the surface of Mars, a space rover with a total mass of 200 kg, wants to return to Earth. Estimate the minimum energy required to return to Earth, assuming that it starts from the distance of 5.3 x 1010m from the centre of the Earth. minimum energy = ………………………….. J [3] SAJC 2021 Preliminary Examination / 9749 [Turn Over

7 2 (a) Explain why a real gas approaches ideal behaviour at very low pressure. ……………….……………….……………….……………….……………….………………… ……………….……………….……………….……………….……………….………………… ……………….……………….……………….……………….……………….………………… ……………….……………….……………….……………….……………….…………….. [2] (b) The variation with pressure p of the volume V of a fixed mass of an ideal gas is shown in Fig. 2.1. The gas undergoes a cycle of changes A to B to C to A. Fig. 2.1 (i) Show that the change from B to C is not an isothermal process. [1] SAJC 2021 Preliminary Examination / 9749 [Turn Over

8 (ii) Calculate the work done on the gas during the change A to B and C to A. work done from A to B = ………………………….. J [3] work done from C to A = ………………………….. J [2] (iii) During the change A to B, 1370 J of thermal energy is transferred to the gas. During the change B to C, no thermal energy enters or leaves the gas. The work done on the gas during this change is 550 J. Complete the table below. Process Heat supplied, Q /J Work done on gas, W / J Change in internal energy, ∆U / J A to B 1370 B to C 0 550 C to A [2] (iv) The cycle of change is now reversed from A to C to B to A. It is now operating as a heat engine, converting some heat energy to useful work. The efficiency of this heat engine is defined as the Efficiency = net work done in a cycle heat absorbed in a cycle Calculate the efficiency of this engine. efficiency = ……………………………. [2] SAJC 2021 Preliminary Examination / 9749 [Turn Over

9 3 (a) Define simple harmonic motion ………….………….………….………….………….………….………….………….………… ………….………….………….………….………….………….………….………….………… ………….………….………….………….………….………….………….………….……... [1] (b) A spring, which hangs from a fixed support, extends by 40 mm when a mass of 0.25 kg is suspended from it. (i) Determine the spring constant k of the spring. spring constant = ………………… N m-1 [1] (ii) An additional mass of 0.44 kg is then placed on the spring and the system is set into vertical oscillations with an amplitude of 20 mm. Given that a = - where a is the acceleration of the mass, x is the displacement of the mass from equilibrium and m is the total mass of the oscillating system. 1. Show that the oscillation frequency is 1.5 Hz. [2] 2. Determine the displacement at which the potential energy and the kinetic energy of the oscillations are equal. displacement = ……………… mm [2] SAJC 2021 Preliminary Examination / 9749 [Turn Over

10 3. With both masses still in place, the spring is now suspended from a horizontal support rod that can be made to oscillate vertically at varying frequencies, as shown in Fig. 3.1. Fig. 3.1 The response of the masses suspended from the spring to the vertical oscillations of the support rod varies with frequency. Describe and explain the motion of the masses when the support rod oscillates at a frequency from 0.2 Hz to 3.0 Hz. ………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………. …………………………………………………………………………………... [4] SAJC 2021 Preliminary Examination / 9749 [Turn Over