2023 RI Prelims P2 QP

© Raffles Institution Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2023 Preliminary Examination PHYSICS Higher 1 Paper 2 Structured Questions 8867/02 September 2023 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your index number, name and class in the spaces at the top of this page. 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 any one question. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use Section A 1 / 5 2 / 9 3 / 10 4 / 7 5 / 9 6 / 20 Section B (circle question attempted) 7 / 8 / 20 Deduction Total / 80 This document consists of 26 printed pages.

2 © Raffles Institution Data speed of light in free space c  3.00 × 108 m s1  elementary charge e  1.60 × 1019 C  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  the Avogadro constant NA  6.02 × 1023 mol1  gravitational constant G  6.67 × 1011 N m2 kg2  acceleration of free fall g  9.81 m s2 Formulae uniformly accelerated motion s  21 2ut at 2v  2 2u as  resistors in series R  R1 + R2 + ….  resistors in parallel 1/R  1/R1 + 1/R2 + ….

3 © Raffles Institution [Turn over Section A Answer ALL questions from this section 1 The acceleration of free fall g can be determined through the period of oscillation T of a simple pendulum of length L. The relationship between these quantities is 2 LT g . In one particular experiment, the following measurements were made. L = (0.850  0.001) m time for 20 oscillations = (36.9  0.2) s (a) Use these measurements to determine a value, to three significant figures, of g. g = m s2 [1] (b) Determine the actual uncertainty in the value of g. Hence, give a statement of g, with its uncertainty, to an appropriate number of significant figures. g =  m s2 [4]

4 © Raffles Institution 2 Tarzan wants to get a coconut from a coconut tree by throwing a stone at the coconut to knock it down. The coconut is 18.0 m above the ground as shown in Fig. 2.1. Tarzan throws a stone such that it hits the coconut horizontally. The stone is projected with an initial speed of 20 m s1 at 2.2 m above the ground. Air resistance is negligible. (a) Determine the angle  to the horizontal at which the stone ha s to be projected so that it will hit the coconut horizontally.  =  [3] (b) Determine the time taken for the stone to reach the coconut at this angle of projection. time taken = s [2] Fig. 2.1 Tarzan 2.2 m 18.0 m 20 m s1 

5 © Raffles Institution [Turn over (c) Hence, calculate the horizontal displacement from the coconut at which Tarzan should project the stone so that it hits the coconut horizontally. horizontal displacement = m [2] (d) If air resistance is not negligible, state and explain how the angle  calculated in (a) and the horizontal displacement calculated in (c) should change so that the stone is still able to hit the coconut horizontally when the stone is projected with the same initial speed. [2]

6 © Raffles Institution 3 (a) Define linear momentum. [1] (b) Two particles A and B with masses 2m and m respectively, move at the same speed u towards each other along a horizontal line and collide elastically. Particle B moves vertically down after the collision and particle A is deflected through an angle  as illustrated in Fig. 3.1. Fig. 3.1 (i) By considering the kinetic energies of both particles, show that: 2 2 2 A B3 2u v v  where vA and vB are the speeds after collision of particles A and B respectively. [1] A B u path of particle B path of particle A  u

7 © Raffles Institution [Turn over (ii) The value of m is 1.7  1027 kg and the value of u is 3.5  105 m s1. 1. By considering the momenta of both particles in the vertical and horizontal directions and using the equation in (b)(i), determine vB. vB = m s1 [3] 2. Hence, calculate the change in momentum of particle B due to the collision. magnitude of change = kg m s1 direction of change = [3]

8 © Raffles Institution (iii) The two particles are in contact for a time of 1.2 s during collision. Determine the average force exerted by particle B on particle A. magnitude of average force = N direction of average force = [2]

9 © Raffles Institution [Turn over 4 (a) State the conditions for a body to be in equilibrium. [2] (b) Define moment of a force. [1] (b) A uniform metre rule of mass 0.090 kg is pivoted at its centre as shown in Fig. 4.1. The left end of the rule is suspended from a fixed point using a spring of force constant 21 N m1. A mass of 0.25 kg is hung from the same end of the rule using a string. A block M is hung from the rule using a string at a distance of 30 cm from the pivot. The rule is horizontal and the extension of the spring is 1.5 cm. Fig 4.1 (i) Show that the mass of block M is 0.36 kg. [2] M spring pivot metre rule 0.25 kg 30 cm

10 © Raffles Institution (ii) Determine the magnitude of the normal contact force acting on the metre rule due to the pivot. magnitude of the normal contact force = N [2]