2024 RI H3 Prelim QP

This document consists of 33 printed pages. © Raffles Institution 9814/01 [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2024 Preliminary Examination PHYSICS (Higher 3) Paper 1 9814/01 24 September 2024 3 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 provided 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, graphs or rough working. Do not use staples, paper clips, glue or correction fluid. The use of approved scientific calculator is expected, where appropriate. Section A Answer all questions. You are advised to spend about 1 hour 50 minutes on Section A. Section B Answer two questions only. You are advised to spend about 35 minutes on each question in Section B. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use 1 (a) / 9 (b) / 6 2 / 6 3 / 6 4 / 6 5 / 6 6 / 8 7 / 6 8 / 7 9 / 20 10 (a) / 10 (b) / 10 11 / 20 Total /100

2 © Raffles Institution 9814/01 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 × 1023 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 2u as+ moment of inertia of rod through one end I = 21 3 ML moment of inertia of hollow cylinder through axis I = ( ) 22 12 1 2 M r r + moment of inertia of solid sphere through centre I = 22 5 MR moment of inertia of hollow sphere through centre I = 22 3 MR work done on/by a gas W = pV hydrostatic pressure p = ρgh gravitational potential  = Gm r− Kepler’s third law of planetary motion T2 =  234 a GM temperature T/K = / C 273.15T + pressure of an ideal gas p = 21 3 Nm c V 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=  −

3 © Raffles Institution 9814/01 [Turn over electric current I = Anvq resistors in series R = 12 ...RR++ resistors in parallel 1/R = 121 1 ...RR++ capacitors in series 1/C = ++121 1 ...CC capacitors in parallel C = ++12 ...CC energy in a capacitor U = 21 2CV electric potential V = 4 Q r  electric field strength due to a long straight wire E =   2 r electric field strength due to a large sheet E =  2 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 energy in an inductor U = I 21 2 L RL series circuits  = L R RLC series circuits (underdamped)  = − 2 2 1 4 R LC L radioactive decay x = ( )0 expxt − decay constant  = 1 2 ln2 t

4 © Raffles Institution 9814/01 Section A Answer all questions in this section. You are advised to spend about 1 hour 50 minutes on this section. 1 (a) Fig. 1.1 shows a ball A of mass Am , moving with velocity Au , makes a head -on and perfectly elastic collision with a ball B of mass Bm , which is initially at rest. before impact after impact Fig. 1.1 After the impact, balls A and B move off with velocities Av and Bv respectively along the line of centres of the balls. (i) Show that, no matter how small the mass of ball B, its speed after the impact cannot exceed A2u [3] A B A B Au Av Bv

5 © Raffles Institution 9814/01 [Turn over (ii) Write down an expression, in terms of Am and Bm , for the fraction f of the initial kinetic energy of ball A which is transferred to ball B. [1] (iii) In another experiment shown in Fig 1.2, ball A is being projected again with velocity Au , towards ball B which is stationary and in contact with another ball C of mass Cm . Fig. 1.2 Ball A strikes ball B, which then knocks forward ball C. All collisions are perfectly elastic. 1. Using your answer to (a)(ii), o btain an expression in terms of Am , Bm and Cm , for the fraction F of the initial kinetic energy of ball A which is transferred to ball C. [1] A B Au C

6 © Raffles Institution 9814/01 2. Hence, in terms of Am and Cm , find the value of Bm which will provide the largest fraction F. [4] Total [9]

7 © Raffles Institution 9814/01 [Turn over (b) Fig 1.3 shows two rigid spheres, P and Q, approaching each other with speeds 1u and 2u respectively in the laboratory frame. Both spheres have the same mass m. Fig. 1.3 (i) Show that the total momentum of the two spheres is zero in the centre -of-mass frame before the collision. [2] (ii) After colliding with each other elastically, they move off to the right with speeds 1v and 2v at the same angle  to the horizontal in the laboratory frame, as shown in Fig. 1.4. Fig. 1.4 1. Show that 12vv= . [1] m m P Q P Q m m

8 © Raffles Institution 9814/01 2. Hence, by considering the velocities of the spheres in the centre -of-mass frame, show that for 60 = , the ratio of the initial speeds of the spheres can be expressed as 1 2 1 1 u u   += − . Determine the value of  .  = [3] Total [6]

9 © Raffles Institution 9814/01 [Turn over 2 Fig 2.1 shows a uniform stick of mass m and length L resting against a rough circular hoop of radius R. The stick makes an angle  with the horizontal and is tangent to the hoop at its upper end at A. Both the hoop and lower end of the stick are resting on the rough ground at points B and C respectively. Point O is the centre of the hoop. (a) Draw and label the normal contact forces NA and NB acting on the hoop by the stick and the ground respectively. Draw and label also, the frictional forces fA and fB acting on the hoop by the stick and the ground respectively. [1] (b) Show that the magnitudes of the frictional forces fA and fB are equal. [1] (c) Show that the normal contact force NA is given by the expression A 1 cos2N mg=  where g is the acceleration due to gravity. Explain your working clearly. [2]  R R A C B O Fi