RVHS 2025 Prelim

RIVER VALLEY HIGH SCHOOL JC 2 PRELIMINARY EXAMINATIONS H3 PHYSICS 9814 24 S EPTEMBER 2025 3 H OURS CANDIDATE NAME CENTRE NUMBER S INDEX NUMBER CLASS 2 4 J INSTRUCTIONS TO CANDIDATES DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Read these notes carefully. Write your name, class and index number above . Write in dark blue or black pen on both sides of the paper. 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 You are advised to spend about 1 hour 50 min on Section A. Section B Answer all questions You are advised to spend about 1 hour 10 min on 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 EXAMINERS’ USE Section A 1 /7 2 /15 3 /8 4 /15 5 /15 Section B 6 /20 7 /20 Deduction TOTAL /100 River Valley High School Page 1 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

________________________________________________________________________ This Question Paper consists of 29 printed pages. River Valley High School Page 2 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

Data speed of light in free space c = 3.00 × 10 8 m s –1 permeability of free space μ 0 = 4 × 10 –7 H m –1 permittivity of free space ε 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 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 moment of inertia of rod through one end Ι = 1 3 𝑀 𝐿 2 moment of inertia of hollow cylinder through axis 𝐼 = 1 2 𝑀 ( 𝑟 1 2 + 𝑟 2 2 )moment of inertia of solid sphere through centre Ι = 2 5 𝑀 𝑅 2 moment of inertia of hollow sphere through centre Ι = 2 3 𝑀 𝑅 2 work done on/by a gas hydrostatic pressure gravitational potential Kepler’s third law of planetary motion 𝑇 2 = 4 π 2 𝑎 3 𝐺𝑀 temperature T / K = T / ° C + 273.15 pressure of an ideal gas River Valley High School Page 3 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

mean translational kinetic energy of an ideal gas molecule displacement of particle in s.h.m. velocity of particle in s.h.m. electric current resistors in series resistors in parallel capacitors in series 1 𝐶 = 1 𝐶 1 + 1 𝐶 2 + … capacitors in parallel 𝐶 = 𝐶 1 + 𝐶 2 + … energy in a capacitor 𝑈 = 1 2 𝐶 𝑉 2 electric potential electric field strength due to a long straight wire 𝐸 = λ 4 π ε 0 𝑟 electric field strength due to a large sheet 𝐸 = σ 2 ε 0 alternating current/voltage magnetic flux density due to a long straight wire magnetic flux density due to a flat circular coil magnetic flux density due to a long solenoid energy in an inductor 𝑈 = 1 2 𝐿 𝐼 2 RL series circuits τ = 𝐿 𝑅 RLC series circuits (underdamped) ω = 1 𝐿𝐶 − 𝑅 2 4 𝐿 2 radioactive decay decay constant River Valley High School Page 4 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

Section A Answer all questions in this section. 1 Ball P strikes ball Q elastically in a head-on collision. The mass of ball Q is twice that of the ball P. (a) By using the centre of mass frame, determine the ratio of the final speed of the ball Q to the initial speed of the ball P. ratio =…………………… [3] (b) Determine the percentage of initial kinetic energy transferred to the ball Q. percentage =…………………… [2] River Valley High School Page 5 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

(c) Determine the number of such collisions that is required to reduce the energy of the ball P from 10 kJ to 0.10 mJ. number of collisions =…………………… [2] River Valley High School Page 6 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

2 (a) (i) A spherical asteroid of radius R is composed entirely of homogeneous titanium of density ρ . A narrow shaft is bored from a point A on the surface of the asteroid to its centre B as shown in Fig. 2.1. Fig. 2.1 Show that the magnitude of the gravitational force acting on a particle of mass m at a distance r from the centre of the asteroid (where r < R ) is given by [2] (ii) A small particle is released from rest at point A and falls through the shaft to B. Determine the speed of the particle on arrival at B [4] River Valley High School Page 7 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

(b) Subsequently, mining removes material so that a spherical cavity of diameter AB = R is formed within the asteroid, as shown in Fig. 2.2. Fig. 2.2 (i) By superposition, show that the gravitational field strength along AB is uniform and determine the magnitude of the field strength. [2] (ii) A second particle is released from rest at A and falls to B. Determine the ratio of its impact speed at B to that found in (a)(ii) . [2] River Valley High School Page 8 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

(c) A rocket ship with mass M 0 and loaded with fuel of mass m 0 takes off vertically in a uniform gravitational field. It ejects fuel with velocity U 0 with respect to the rocket ship. The ship is completely ejected during a time t 0 . (i) Derive an equation of motion of the rocket in terms of , U 0 , g and M , where M is the mass of the rocket at time t . [2] (ii) Hence, determine the velocity of the vehicle at the instant t 0 when all the fuel has been ejected, in terms of M 0, m 0 , g and t 0. River Valley High School Page 9 of 29 H3 Physics 9814 JC 2 Preliminary Examinations 2025

[3] 3 (a) A parallel plate capacitor has capacitance C . By considering the work dw needed to transport a small amount of charge dq from one plate to another, derive an expression for the electric potential energy U stored in the parallel plate capacitor in terms of the charge Qstored in the capacitor and its capacitance C . Show your working clearly. [3] (b) In the circuit shown in Fig. 3.1, you may assume that the capacitors, battery and inductors have no resistance