RI 2026 H3 Physics Prelim

This document consists of 39 printed pages. © Raffles Institution 9814/01 [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2026 Preliminary Examination PHYSICS (Higher 3) Paper 1 9814/01 29 September 2026 3 hours You must answer on the Question Paper. No additional materials are needed. INSTRUCTIONS • Section A: answer all questions • Section B: answer two questions • Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. • Write your name, centre number and index number in the boxes at the top of the page. • Write your answer to each question in the space provided. • Do not use an erasable pen. Do not use correction fluid or tape. • Do not write on any bar codes. • You may use an approved calculator. INFORMATION • The total mark for this paper is 100. • The number of marks for each question or part question is shown in brackets [ ] For Examiner’s Use 1 / 7 2 / 6 3 / 7 4 / 6 5 / 8 6 / 6 7 / 10 8 / 10 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 ( 0 1 4 = 8.99 × 109 mF−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+ work done on/by a gas W = pV 2v = 2 2u as+ pressure p = F A moment of inertia of rod through one end I = 21 3 ML gravitational potential  = Gm r− moment of inertia of hollow cylinder through axis I = ( ) 22 12 1 2 M r r + temperature T/K = / C 273.15T + moment of inertia of solid sphere through centre I = 22 5 MR pressure of an ideal gas p = 21 3 Nm c V moment of inertia of hollow sphere through centre I = 22 3 MR mean translational kinetic energy of an ideal gas particle E = 3 2 kT displacement of particle in s.h.m. x = 0 sinxt  magnetic flux density due to a long straight wire B = 0 2 d   I velocity of particle in s.h.m. v = 0 cosvt  magnetic flux density due to a flat circular coil B = 0 2 N r  I = 22 0xx− magnetic flux density due to a long solenoid B = 0n I electric current I = nAvq energy in an inductor U = I 212 L resistors in series R = 12 ...RR++ RL series circuits  = L R

3 © Raffles Institution 9814/01 [Turn over resistors in parallel 1/R = 121 1 ...RR++ RLC series circuits (underdamped)  = − 2 2 1 4 R LC L capacitors in series 1/C = ++121 1 ...CC energy states for quantum particle in a box nE = 2 2 28 h nmL capacitors in parallel C = ++12 ...CC radioactive decay x = ( )0 expxt − energy in a capacitor U = 1 2QV radioactive decay constant  = 1 2 ln2 t = 21 2 Q C Lorentz factor  = 2 1 1 vc− = 21 2CV length contraction L = 0L  charging a capacitor Q = 0 1 t Qe −−  time dilation T = 0T discharging a capacitor Q = 0 t Qe − Lorentz transformation equations 'x = ( )x vt − RC time constant  = RC 't = 2 vxt c − electric potential V = 4 Q r velocity addition 'u = ( ) 21 uv uv c −  − electric field strength due to a long straight wire E =  2 r mass−energy equivalence 2E = ( ) ( ) 22 2pc mc+ electric field strength due to a large sheet E =  2 alternating current/voltage x = 0 sinxt 

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 Fig. 1.1 shows the principle of operation of a linear accelerator, a machine used to accelerate charged particles to high speeds so they can initiate nuclear reactions. The particles are injected along the axes of cylindrical metal tubes 1T , 2T , … 5T , with gaps of fixed width d between adjacent tubes. Alternate tubes are connected together, and the two sets are connected to an alternating voltage supply of frequency f. Inside a tube, the particle travels at constant speed and spends exactly one half-cycle of a period inside each tube. When it reaches a gap, it is accelerated across to the next tube. Fig. 1.1 A charged particle of mass m is injected into tube T1 with initial speed u. At each gap, a constant force F acts on the particle over the gap. (a) Show that the speed of the particle upon entering the nth tube is given by the expression 2 2( 1) n n Fdvu m−=+ [Hint: you may wish to use the chain rule where dy dy dz dx dz dx= ] particle source vacuum metal tubes a.c. voltage supply particle accelerates between tubes half cycle T1 T2 T3 T4 T5 particles moving at high speeds supply

5 © Raffles Institution 9814/01 [Turn over [2] (b) The particle exits the accelerator and undergoes an inelastic collision with a stationary target particle of mass M. The kinetic energy lost during the collision is E. Express the minimum kinetic energy the particle must have before the collision in terms of E, m and M. [2]

6 © Raffles Institution 9814/01 (c) A particle is injected with an initial speed of 611.5 10 m s − into an accelerator where the force acting across each gap is 148.0 10 N− over a gap width of 25.0 10 m− . The particle then collides with a stationary target particle of mass 276.68 10 kg− and loses 132.0 10 J− of kinetic energy. If the minimum number of tubes required is 63, determine the mass of the particle. mass of particle = kg [3] [Total: 7]

7 © Raffles Institution 9814/01 [Turn over 2 (a) Block A of mass 50 kg rests on a plane that is inclined at an angle  to the horizontal as shown in Fig 2.1. Block B of mass M kg is placed on top of block A. Fig 2.1 The two blocks are at rest at limiting friction and the coefficient of static friction between the two blocks and between block A and the inclined plane is 0.30. Determine the value of  . Explain your working clearly.  =  [2] (b) The blocks are now placed on another inclined plane that is 30 to the horizontal and are connected by a light inextensible string over a rough cylinder as shown in Fig 2.2. The coefficient of static friction between the two blocks and between block A and the inclined plane is still 0.30. Fig 2.2 30 

8 © Raffles Institution 9814/01 The tension acting on block A, AT and the tension acting on block B, BT are related by the equation BAT =T e  , where  is the angle subtended by the string on the cylinder in radians. The coefficient of friction  between the string and the cylinder is 0.20. Determine the value of M when the blocks are at limiting friction with block A just about to