HCI 2026 H3 Physics Prelim

This document consists of 33 printed pages. HWA CHONG INSTITUTION 9814 / H3 Preliminary Examination CANDIDATE NAME CENTRE NUMBER INDEX NUMBER PHYSICS Paper 1 Candidates answer on the Question Paper. No Additional Materials are required. 9814/01 21 September 2026 3 hours READ THESE INSTRUCTIONS FIRST Write your Centre number, index number and name 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, graphs or rough working. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use 1 9 2 16 3 9 4 6 5 20 6 20 7 20 8 20 Deductions Total 100

2 © Hwa Chong Institution 9814 H3 Physics / Preliminary Exam 2026 Data speed of light in free space c = 813.00 10 m s − permeability of free space 0 = 714 10 H m −− permittivity of free space 0 = ( )( ) 12 1 91 8.85 10 F m 1/ 36 10 F m −− −−   0 1 4 = 918.99 10 m F − elementary charge e = 191.60 10 C− Planck constant h = 346.63 10 J s− unified atomic mass constant u = 271.66 10 kg− rest mass of electron em = 319.11 10 kg− rest mass of proton pm = 271.67 10 kg− molar gas constant R = 118.31 J K mol−− Avogadro constant AN = 23 16.02 10 mol − Boltzmann constant k = 23 11.38 10 J K−− gravitational constant G = 11 2 26.67 10 N m kg−− acceleration of free fall g = 29.81 m s− Formulae uniformly accelerated motion 21 2s ut at=+ work done on / by a gas W p V= 22 2v u as=+ pressure Fp A= moment of inertia of rod through one end 21 3 ML=I gravitational potential GM r =− moment of inertia of hollow cylinder through axis ( ) 22 12 1 2 M r r=+I temperature / K / C 273.15TT =  + moment of inertia of solid sphere through centre 22 5 MR=I pressure of an ideal gas 21 3 Nmpc V= moment of inertia of hollow sphere through centre 22 3 MR=I mean translational kinetic energy of an ideal gas molecule 3 2E kT=

3 © Hwa Chong Institution 9814 H3 Physics / Preliminary Exam 2026 displacement of particle in s.h.m. 0 sinx x t = magnetic flux density due to a long straight wire 0 2B d= I velocity of particle in s.h.m. 0 cosv v t = ( ) 22 0xx= − magnetic flux density due to a flat circular coil 0 2 NB r= I electric current nAvq=I magnetic flux density due to a long solenoid 0Bn = I resistors in series 12 ...R R R= + + resistors in parallel 12 1 1 1 ...R R R= + + energy in an inductor 21 2UL= I capacitors in series 12 1 1 1 ...C C C= + + RL series circuits L R = capacitors in parallel 12 ...C C C= + + RLC series circuits (underdamped) 2 2 1 4 R LC L =− energy in a capacitor 1 2U QV= energy states for quantum particle in a box 2 2 28n hEn mL= 21 2 QC= radioactive decay ( )0 expx x t =− 21 2CV= radioactive decay constant 1 2 ln2 t = charging a capacitor 0 1 t Q Q e −=−   Lorentz factor 2 1 1 vc  = − discharging a capacitor 0 t Q Q e −= length contraction 0LL = RC time constant RC = time dilation 0TT = electric potential 04 QV r= Lorentz transformation equations (1 dimension) ( )x x vt=− electric field strength due to a long straight wire 02E r= 2 vxtt c=−  electric field strength due to a large sheet 02E = velocity addition ( ) 21 uvu uv c −= − alternating current/voltage 0 sinx x t = mass-energy equivalence ( ) ( ) 2222E pc mc=+

4 © Hwa Chong Institution 9814 H3 Physics / Preliminary Exam 2026 Section A Answer all questions in this section. You are advised to spend about 1 hour 50 minutes on this section. 1 A 5.0 kg mass P moving due East with a velocity of 5.00 m s-1 collides elastically with a 10.0 kg mass Q moving in a North-West direction with a velocity of 10.00 m s-1 as shown in Fig. 1.1. (a) Determine the horizontal and vertical components of the velocity of centre of mass frame relative to Earth. horizontal component of velocity = ………..………………….. m s-1 vertical component of velocity = ………..………………….. m s-1 [2] P Q Fig. 1.1 45 o North

5 © Hwa Chong Institution 9814 H3 Physics / Preliminary Exam 2026 (b) Determine the magnitude of velocity of P in the centre of mass frame before the collision. velocity of P = ………………………. m s-1 [2] (c) After the collision, Q moves due North in the centre of mass frame. (i) Explain why, in this frame, the mass P moves due South with same speed in (b) after the collision. ..……………………………………..………………………………………………………….….. ..……………………………………..………………………………………………………….….. …..……………………………………..……………………………………………………….….. ……..……………………………………..…………………………………………………….….. ………..………………………………………………………………………………………… [2] (ii) Determine the magnitude and direction of the velocity of P in the Earth’s reference frame after the collision. magnitude = ………………………. m s-1 [2] direction = …………………………….. [1] [Total: 9 marks]

6 © Hwa Chong Institution 9814 H3 Physics / Preliminary Exam 2026 2 A DC voltage booster is used to increase the output voltage above the electromotive force (e.m.f.) of a DC source in a circuit. A simple DC voltage booster circuit is shown in Fig. 2.1. It consists of a source of e.m.f.  , a resistor of resistance R, an inductor of inductance L, a capacitor of capacitance C, a switch S and a diode. (a) After the circuit is built, the switch S is closed for the first time, and the steady state is reached. State (i) an expression for the current i0 in the inductor in terms of  and R. ………………………………………………………………………………………………… [1] (ii) an expression for the charge q on the capacitor in terms of  and C. ………………………………………………………………………………………………… [1] Fig. 2.1  output voltage R S L C diode

7 © Hwa Chong Institution 9814 H3 Physics / Preliminary Exam 2026 (b) Switch S is then opened at t = 0. The charge q on the capacitor and the current i in the circuit are such that 0di qL dt C − − + = (i) Show that 2 2 d i i LCdt =− [1] (ii) Show that the solution to the equation in (b)(i) is 0 sin( )i i t =+ where i0 and  are constants, and 1 LC = . [2]

8 © Hwa Chong Institution 9814 H3 Physics / Preliminary Exam 2026 (iii) By using the equation 0di qL dt C − − + = at t = 0, 1. show that 0didt = [1] 2. hence show that 2  = [1] (iv) After the switch S is opened, 1. describe the variation in the current through the inductor, ………………………………………………………………………………………………. ……………………………………………………………………………………