2021 RI Yr CT Sect B QP

© Raffles Institution 9749 Name: ( ) CT Group: 22S0 RAFFLES INSTITUTION 2021 YEAR 5 TERM 3 COMMON TEST 30 June 2021 H2 PHYSICS RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES Section B INSTRUCTIONS TO CANDIDATES Write your name, index number and CT Group. Write your answers to Section B in the spaces provided on the question paper. You are advised to write all your workings and answers clearly. Marks may be deducted for unclear workings. For Examiner’s Use Section A MCQ / 15 Section B 1 / 10 2 / 11 3 / 11 4 / 11 5 / 12 6 / 11 7 / 14 Deductions Total / 95 This document consists of 19 printed pages.

2 © Raffles Institution 9749 [Turn over Section B (80 marks) 1 An equation that governs gas-flow through a cylindrical tube is given by ( ) 3 12cr p p mZ L RT −= , where c is a unitless constant, r is the internal radius of the tube, p 1 and p2 are the pressures at the ends of the tube, L is the length of the tube, m is the molar mass of the gas (in kg mol−1), R is the molar gas constant (in kg m2 s−2 K−1 mol−1), and T is the thermodynamic temperature of the gas. (a) Show that the SI base unit of pressure is kg m−1 s−2. [1] (b) Determine the SI base unit of the quantity Z. base unit = [2] (c) Experiments on gas -flow through a cylindrical tube are conducted. The pressure difference (p1 − p2) between two points along the tube is recorded as 800 101 Pa by a pressure gauge as shown in Fig.1.1 . However, the manufacturer of the pressure gauge states that its measurements have a percentage uncertainty of 2.5%. Fig. 1.1 p1 p2 pressure gauge

3 © Raffles Institution 9749 [Turn over (i) Determine the absolute uncertainty in the value of (p1 − p2). absolute uncertainty = Pa [2] (ii) Hence, state (p1 − p2), with its uncertainty, to an appropriate number of significant figures in terms of MPa. (p1 − p2) = ± MPa [1] (d) In addition to the information given in (c), the internal diameter d is found to be (3.34 ± 0.03) mm and the length L is found to be (0.153 ± 0.001) m. It is estimated that the percentage uncertainties in temperature T and molar mass m are 2.8% and 1. 7%, respectively, due to random errors. (i) Distinguish between systematic errors and random errors in the measurement of a physical quantity. [2] (ii) Determine the percentage uncertainty in the value of Z. percentage uncertainty = % [2]

4 © Raffles Institution 9749 [Turn over 2 (a) In the 1992 Barcelona Olympics opening ceremony, an archer stood at a distance of 60 m from the base of a tower. The archer shot a flaming arrow at an angle θ from the horizonal to light the Olympic cauldron on top of the tower that is 24 m above him . The flaming arrow lit the cauldron at the peak of its trajectory as shown in Fig. 2.1. Fig. 2.1 (i) Show that the arrow took 2.2 s to reach the cauldron. Ignore air resistance. [3] (ii) Calculate the initial horizontal speed of the arrow. horizontal speed = m s–1 [2] (iii) Determine the angle θ. θ = ° [2] cauldron 24 m θ tower 60 m archer trajectory of arrow

5 © Raffles Institution 9749 [Turn over (b) A cart carrying a ball accelerates down a long plane inclined at an angle φ to the horizontal as shown in Fig. 2.2. The cart then launches the ball such that the ball’s initial velocity with respect to the cart is perpendicular to the motion of the cart. The ball is under free fall after it was launched from the cart. Fig. 2.2 (i) On Fig. 2.2, sketch the trajectory of the ball after it was launched from the cart, as viewed by a person on the ground. [1] (ii) Express the cart’s acceleration along the plane in terms of φ and the acceleration of free fall g. acceleration = [1] (iii) By comparing the component of the ball’s acceleration that is parallel to the plane with your answer in (b)(ii), state and explain whether the ball will land back on the cart. [2]

6 © Raffles Institution 9749 [Turn over 3 Balls A and B are t wo identical balls , each of mass 0.22 kg and radius 0.030 m . The initial distance between the centres of the balls is 0.950 m. The balls then move towards each other head on with an initial speed of 0.20 m s −1 as shown in Fig. 3.1. All surfaces are assumed to be frictionless. Fig. 3.1 (a) Determine the time taken for the balls to come in contact. time taken = s [2] (b) The balls collide and are in contact for 0.070 s before they reverse their direction of motion and move off with the same speed as each other. During the collision, 20% of the kinetic energy of the balls is lost as thermal energy. (i) State with a reason the type of collision the balls underwent. [1] (ii) Calculate the speed of the balls after collision. speed = m s−1 [2] 0.950 m 0.20 m s−1 0.20 m s−1 ball A ball B

7 © Raffles Institution 9749 [Turn over (iii) Calculate the magnitude of the average force acting on ball A during its collision with ball B. magnitude of average force = N [2] (iv) 1. On Fig 3.2, sketch separate graphs for ball A and ball B to show the variation with time t of each ball’s acceleration a. Your graphs should be for the duration when balls A and B were initially 0.950 m apart at t = 0 to after they collide and move off. Include appropriate values of t and label your graphs A and B for balls A and B respectively. Fig 3.2 [2] a / m s−2 t / s 0

8 © Raffles Institution 9749 [Turn over 2. If the mass of ball A is now greater than the mass of ball B, sketch on Fig. 3.3, a new set of graphs to show the variation with time t of each ball’s acceleration a, over the same duration as in (b)(iv)1. Include appropriate values of t and label your graphs A’ and B’ for balls A and B respectively. Fig 3.3 Using Newton’s laws of motion, explain how your graphs A’ an