2024 TJC H2 Prelim Paper 2 with solutions (QP + ANS)

TEMASEK JUNIOR COLLEGE 2024 JC2 Preliminary Examination Higher 2 NAME CG PHYSICS Paper 2 Structured Questions 9749/02 23 August 2024 2 hours For Examiner’s Use READ THESE INSTRUCTIONS FIRST 1 Write your name and civics group in the spaces at the top of this page. 2 Write in dark blue or black pen on both sides of the paper. 3 You may use an HB pencil for any diagrams or graphs. 4 Do not use staples, paper clips, glue or correction fluid. 5 The use of an approved scientific calculator is expected, where appropriate. 6 Answer all questions 7 s.f The number of marks is given in brackets [ ] at the end of each question or part question. Total This booklet consists of 21 printed pages

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 Answer all the questions in the spaces provided. 1 (a) State the conditions for a body to be in equilibirum. 1. 2. [2] (b) An athlete uses a machine in the gym where he hinges at the knee joint to move his lower legs up as shown in Fig. 1.1. There is a constant downward force of 25 N exerted at point A on each feet at constant distance L from point B, as shown in Fig. 1.2. The combined weight of a foot and one lower leg is 30 N acting at L/2 from the knee joint. When the legs are raised, there is a force F at distance L/4 from knee joint and at angle of  to the leg as shown in Fig 1.2. Fig. 1.1 Fig 1.2 It is given that L = 40 cm. At position shown in Fig. 1.2, the lower leg and feet are at equilbrium at angle of 55° to the vertical, and  = 25°. (i) By taking moments about point B at the knee joint, calculate the force F exerted on the lower leg in Fig 1.2. force, F = N [2] knee joint F 30 N 25 N B A point A

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 4 (ii) For the lower leg to be in equilibrium, there is a force R at the knee joint. Draw on Fig.1.2, a labelled arrow to represent the force R. [1] (iii) At the beginning, the feet are down as shown in Fig. 1.3. He raises his legs until they are at an angle of 55 ° to the vertical as shown in Fig. 1.4. Calculate the work done to raise one lower leg to this position at constant speed. Assume that the knee joint is a point that stays in place throughout. [2] (iv) Hence calculate the power exerted by the athlete in raising one leg to the position shown in Fig 1.4 if the time taken is 5.0 s. Power exerted = W [1] L Fig 1.3 Fig 1.4 25 N

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 5 [Turn over 2 (a) (i) Explain why the gravitational potential at a point in a gravitational field is negative. [2] (ii) The gravitational potential at the surface of Earth is -62.6  106 J kg -1, and that at the surface of Moon is -28.1  106 J kg-1. (The mass of the Earth is 81 times the mass of the Moon). 1. On Fig. 2.1, sketch a graph which shows the variation of gravitational field strength along a line from the surface of Earth to the surface of Moon. [2] 2. Hence sketch, on Fig. 2.2, a graph which shows the variation of gravitational potential along a line from the surface of Earth to the surface of Moon. [2] Moon Earth Fig. 2.1 Fig. 2.2 Distance from surface of Earth Distance from surface of Earth Gravitational field strength Gravitational potential

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 6 (b) An isolated spherical planet has a diameter of 6.8 × 10 6 m. Its mass of 6.4 × 10 23 kg may be assumed to be a point mass at the centre of the planet. (i) Show that the gravitational field strength at the surface of the planet is 3.7 N kg-1. [1] (ii) A stone of mass 2.4 kg is raised from the surface of the planet through a vertical height of 1800 m. Use the value of the field strength from (i) to determine the change in gravitational potential energy of the stone. Explain your working. change in gravitational potential energy = J [2] (iii) A rock, initially at rest at infinity, moves towards the planet. At point P, its height above the surface of the planet is 3.5 D, where D is the diameter of the planet, as shown in Fig. 2.3. Fig. 2.3 Calculate the speed of the rock at point P. Explain your working, speed at point P = m s-1 [3]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 7 [Turn over 3 A horizontal string is stretched between two fixed points A and B. A vibrator is used to oscillate the string and produce an observable stationary wave. At one instant, the moving string is straight, as shown in Fig. 3.1. The dots in the diagram represents the positions of the nodes on the string. Point P, which is in the middle of the 2 adjacent dots on the string is moving downwards. The wave on the string has a speed of 35 m s-1 and period of 0.040 s. (a) Explain how the stationary wave is produced. [2] (b) On Fig. 3.1, sketch a line to show a possible position of the string a quarter of a cycle later than the position shown on the diagram. [1] (c) Determine the horizontal distance from A to B. distance = m [2] (d) A particle on the string has zero displacement at t = 0 s. From time t = 0 to time = 0.060 s, the particle moves through a total distance of 72 mm. (i) Calculate the amplitude of oscillation of the particle. amplitude = mm [2] Fig. 3.1

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