2023 RI H2 Physics Prelims P2 Questions

Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2023 Preliminary Examination PHYSICS Higher 2 Paper 2 Structured Questions 9749/02 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. Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use 1 / 9 2 / 10 3 / 8 4 / 7 5 / 10 6 / 10 7 / 6 8 / 20 Deduction Total / 80 This document consists of 23 printed pages.

2 Data speed of light in free space c = 81 3.00 10 m s −  permeability of free space 0 = 71 4 10 H m −−  permittivity of free space 0 = 12 1 8.85 10 F m −−  ( )( ) 91 1 36 10 F m −−  elementary charge e = 19 1.60 10 C −  the Planck constant h = 34 6.63 10 J s −  unified atomic mass constant u = 27 1.66 10 kg −  rest mass of electron me = 31 9.11 10 kg −  rest mass of proton mp = 27 1.67 10 kg −  molar gas constant R = 1 18.31 J K mol − − the Avogadro constant NA = 23 16.02 10 mol − the Boltzmann constant k = 23 11.38 10 J K − − gravitational constant G = 11 226.67 10 N m kg − − acceleration of free fall g = 29.81 m s− Formulae uniformly accelerated motion s = 21 2ut at+ 2v = 2 2u as+ work done on / by a gas W = pV hydrostatic pressure p = ρgh gravitational potential  = Gm r− temperature T / K = / C 273.15T + pressure of an ideal gas p = 21 3 Nm cV mean translational kinetic energy of an ideal gas molecule E = 3 2 kT displacement of particle in s.h.m. x = 0 sinxt  velocity of particle in s.h.m. v = 0 cosvt  22 0xx=  − electric current I = Anvq resistors in series R = 12 RR++ resistors in parallel 1/R = 1/R1 + 1/R2 + …. electric potential V = 4 Q r  alternating current/voltage x = 0 sinxt  magnetic flux density due to a long straight wire B = 0 2 d   I magnetic flux density due to a flat circular coil B = 0 2 N r  I magnetic flux density due to a long solenoid B = 0n I radioactive decay x = ( )0 expxt − decay constant  = 1/2 ln2 t

3 © Raffles Institution [Turn over Answer all the questions in the spaces provided. 1 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. 1.1. 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. 1.1 Tarzan 2.2 m 18.0 m 20 m s−1 

4 (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]

5 © Raffles Institution [Turn over 2 (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. 2.1. Fig. 2.1 (i) By considering the kinetic energies of both particles, show that: 2 2 2 AB32u 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

6 (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]

7 © Raffles Institution [Turn over (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]

8 3 (a) State the conditions for a body to be in equilibrium. [2] (b) A uniform metre rule is pivoted at its centre as shown in Fig. 3.1. 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. 3.1 (i) Show that the mass of block M is 0.36 kg. [2] M spring pivot metre rule 0.25 kg 30 cm

9 © Raffles Institution [Turn over (ii) Block M is now shifted to the end of the rule as shown in Fig. 3.2. To keep the rule horizontal, half of block M is submerged in a liquid of unknown density. The density of block M is 8.9  103 kg m−3. Fig. 3.2 Determine the density of the liquid. density of liquid = kg m−3 [3] (iii) Without further calculation, describe the equilibrium positions of the metre rule and block M when the spring in Fig. 3.2 is removed. [1] M spring pivot metre rule 0.25 kg liquid

10 4 (a) State what is meant by a longitudinal wave. [1] (b) Fig. 4.1 shows the equilibrium positions of 14 equally spaced air molecules, labelled 1 to 14, along a line AB. The separation between two adjacent equilibrium positions is 0.020 m. When a point source of sound located on the left of A is switched on, a sinusoidal sound wave travels through the air at a speed of 343 m s−1. At time t = 0 s, air molecule 4 is at its maximum displacement towards the right from its equilibrium position, while air molecule 8 is the closest molecule that is at its maximum displacement towards the left. (i) Determine, for the sound wave, 1. its wavelength wavelengt