RI 2025 Prelim

Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2025 Preliminary Examination PHYSICS (Higher 3) Paper 1 9814/01 25 September 2025 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) / 8 (b) / 7 2 / 6 3 / 5 4 / 8 5 / 6 6 / 6 7 / 6 8 / 8 9 / 20 10 (a) / 10 (b) / 10 This document consists of 34 printed pages. © Raffles Institution 9814/01 [Turn over

2 11 / 20 Total /100 Data speed of light in free space c = 3.00 × 10 8 m s − 1 permeability of free space = 4 π × 10 − 7 H m − 1 permittivity of free space = 8.85 × 10 − 12 F m − 1 = (1/(36 π )) × 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 m e = 9.11 × 10 − 31 kg rest mass of proton m p = 1.67 × 10 − 27 kg molar gas constant R = 8.31 J K − 1 mol − 1 the Avogadro constant N A = 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 m 2 kg − 2 acceleration of free fall g = 9.81 m s − 2 Formulae uniformly accelerated motion s = = moment of inertia of rod through one end I = moment of inertia of hollow cylinder through axis I = moment of inertia of solid sphere through centre I = moment of inertia of hollow sphere through centre I = © Raffles Institution 9814/01

3 work done on/by a gas W = hydrostatic pressure p = ρ gh gravitational potential φ = Kepler’s third law of planetary motion T 2 = temperature T/K = pressure of an ideal gas p = mean translational kinetic energy of an ideal gas molecule E = displacement of particle in s.h.m. x = velocity of particle in s.h.m. v = electric current I = Anvq resistors in series R = resistors in parallel 1/R = capacitors in series 1/C = capacitors in parallel C = energy in a capacitor U = electric potential V = electric field strength due to a long straight wire E = electric field strength due to a large sheet E = alternating current/voltage x = magnetic flux density due to a long straight wire B = magnetic flux density due to a flat circular coil B = magnetic flux density due to a long solenoid B = © Raffles Institution 9814/01 [Turn over

4 energy in an inductor U = RL series circuits τ = RLC series circuits (underdamped) ω = radioactive decay x = decay constant λ = © Raffles Institution 9814/01

5 Section A Answer all questions in this section. You are advised to spend about 1 hour 50 minutes on this section. 1 (a) A metal sphere is dropped from a height h onto a metal plate. The sphere makes impact with the plate repeatedly, each time rebounding to a lesser height. At each impact, the sphere loses a constant fraction F of the kinetic energy possessed by the sphere just before the collision. (i) Write down an expression for 1. F in terms of and , where is the speed of the sphere just before the n th impact and is the speed of the sphere immediately after the n th impact. [1] 2. t , the time interval between the n th and ( n + 1)th impacts in terms of and g . Neglect air resistance. © Raffles Institution 9814/01 [Turn over

6 [1] (ii) Hence, show that the sphere comes to rest in a finite time T after being released is given by the expression [Hint: for ] [4] (iii) Determine F for the sphere when it is dropped from a height of 1.2 m when it comes to rest 8.2 s after release. © Raffles Institution 9814/01

7 [2] 1 (b) Fig. 1.1 shows two meteorites, A and B, travelling towards each other in deep space. A, with a mass of 1.0 kg, is travelling horizontally to the right with a speed of 4.0 m s –1 . B, with a mass of 3.0 kg, is travelling vertically downwards with a speed of 1.0 m s –1 . Fig. 1.1 (i) Show that the velocity of the centre of mass of the two meteorites, v CM , is at an angle of 36.9° clockwise below the horizontal. [3] (ii) A and B then collide and stick together to form a combined meteorite. Explain why the combined meteorite must be moving at the velocity v CM after its formation. © Raffles Institution 9814/01 [Turn over

8 [1] © Raffles Institution 9814/01

9 (iii) The combined meteorite, moving at velocity v CM , then strikes a spaceship travelling in space at a speed of 9.0 m s –1 , at an angle of anti-clockwise above the horizontal. An astronaut on the spaceship observes the combined meteorite striking the spaceship from a vertically downwards direction (i.e. in the same direction that B was initially travelling in). Determine . = ° [3] Total [15 marks] © Raffles Institution 9814/01 [Turn over

10 2 Fig. 2.1 shows a book of mass M that is pressed against a vertical wall by a force F which makes an angle θ with respect to the horizontal. The coefficient of static friction between the book and the wall is μ . The book is stationary. Fig 2.1 (a) On Fig. 2.1, draw and label the weight Mg , frictional force f and normal contact force N acting on the book. [1] (b) Show that the force F is given by © Raffles Institution 9814/01