2021 RI Prelims H2 Phy Paper 3 QP

© Raffles Institution [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2021 Preliminary Examination PHYSICS Higher 2 Paper 3 Longer Structured Questions 9749/03 September 2021 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 in the spaces provided in this booklet. 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 one question only. You are advised to spend one and a half hours on Section A and half an hour on Section B. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use Section A 1 / 8 2 / 8 3 / 9 4 / 10 5 / 6 6 / 11 7 / 8 Section B 8 / 9 / 20 Deduction Total / 80 This document consists of 22 printed pages.

2 © Raffles Institution Data speed of light in free space c  3.00 × 108 m s1 permeability of free space 0  4   107 H m1 permittivity of free space 0  8.85 × 10 12 F m1  (1/(36 )) × 109 F m1 elementary charge e  1.60 × 10 19 C the Planck constant h  6.63 × 10 34 J s 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 molar gas constant R  8.31 J K 1 mol1 the Avogadro constant NA  6.02 × 10 23 mol1 the Boltzmann constant k  1.38 × 10 23 J K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 2ua s work done on/by a gas W  p V 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 2kT   displacement of particle in s.h.m. x  0 sinx t velocity of particle in s.h.m. v  0 cosvt  22 0x x  electric current I  Anvq resistors in series R  12 ...RR resistors in parallel 1/ R  121 1 ...RR electric potential V  4 Q r alternating current/voltage x  0 sinx t 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 Section A Answer all the questions from this Section in the spaces provided. 1 (a) A body has an initial velocity u and a constant acceleration a in the same direction. After time t, the body has moved a distance s and has a final velocity v. The motion can be summarised by the following equations 1 2 vua t su v t   Using the above equations, derive an expression for v in terms of u, a and s. [1] (b) Fig. 1.1 shows a basketball player practici ng a layup where the basketball of diameter 0.23 m is tossed vertically upwards close to the rim of the hoop into the hoop. Determine the minimum vertical velocity of release required in order for the basketball to enter the basket when it is thrown upwards from a height of 2.1 m. minimum vertical velocity = m s –1 [3] 3.0 m 2.1 m Fig. 1.1

4 © Raffles Institution (c) Fig. 1.2 shows another basketbal l player taking a jumpshot from the three-point line of a basketball court. He releases the basketball at an angle of 50  above the horizontal with speed u at line A at a height of 2.5 m above the ground. The hoop is at line B, 3.0 m above the ground and 6.7 m from line A. The basketball takes 1.3 s to travel from line A to line B. (i) Show that the speed u is 8.0 m s 1. [1] (ii) Hence, calculate the height of the basketball above the ground at line B. height = m [3] 3.0 m 6.7 m u 2.5 m 50 A B Fig. 1.2

5 © Raffles Institution [Turn over 2 (a) Explain why gravitational potential has a negative value. [2] (b) Fig. 2.1 shows the variation of the gravitational potential  with distance d from the surface of a certain planet. Point P is at a distance of 1.0  107 m from the surface of the planet and point Q is on the surface of the planet. (i) Determine the gravitational acceleration at point P. gravitational acceleration = m s 2 [2] -50 -40 -30 -20 -10 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 d / 10 7 m  / MJ kg1 P Q Fig. 2.1

6 © Raffles Institution (ii) Assuming that a 1.0 kg mass falls from point P toward point Q with the acceleration obtained in (b)(i) throughout the motion, calculate the increase in its kinetic energy. increase in kinetic energy = J [2] (iii) Indicate, using vertical double-head arrows, the parts of the graph that represent 1. your answer in (b)(ii). Label this arrow A. 2. the actual increase in the kinetic ener gy of the 1.0 kg mass when the gravitational acceleration from P to Q is not constant. Label this arrow B. [2]

7 © Raffles Institution [Turn over 3 (a) State how the temperature of an ideal gas is related to the energy of its molecules. [1] (b) An oven with volume 0.029 m 3 contains air at a pressure and temperature of 1.0  105 Pa and 27C respectively. The mass of one mole of air is 0.030 kg. Assume that the air behaves as an ideal gas. (i) Determine the root-mean-square speed of the air molecules in the oven. root-mean-square speed = m s 1 [2] (ii) Calculate the number of moles of air molecules in the oven. number of moles = [2] (iii) The oven is heated to a temperature of 220C. Use your answer in (a) and the kinetic theory of gases to explain why the pressure of the air in the oven increases. [2]

8 © Raffles Institution (iv) The oven door is opened. Calculate the mass of air that must escape from the oven for the pressure in the oven to return to 1.0  10 5 Pa. mass of air = kg [2]

9 © Raffles Institution [Turn over 4 (a) Fig. 4.1 shows the equilibrium and actual positi ons at an instant in time of a series of particles forming part of a stationary sound wave. Particle M is at its maximum displacement. On Fig. 4.2, (i) sketch the variation with distance of the displacement of the particles at the instant shown, taking motion to the right as positive. Label your sketch P. [2] (ii) sketch the variation with distance of the displacement of the particles at one-quarter of a period later. Label your sketch Q. [1] (iii) indicate the position of one displacement antinode with A and the position of one displacement node with N. [1] (b) The stationary wave in (a) is formed in a pipe of length 0.40 m that is closed at one end and open at the other. An incident sound wave of frequency 1060 Hz travels parallel to the axis of the pipe, and enters the pipe, as shown