NYJC EJC 2024 Prelim

EUNOIA JUNIOR COLLEGE, NAN YANG JUNIOR COLLEGE JC2 Preliminary Examination 2024 General Certificate of Education Advanced Level Higher 3 CANDIDATE NAME CIVICS GROUP 2 3 - REGISTRATION NUMBER PHYSICS Paper 1 9814/01 19 September 2024 3 hours Candidates answer on the Question Paper. For Examiner’s Use Section A 1 13 2 10 3 10 4 10 5 7 6 10 Section B 7 20 8 20 9 20 s.f. Total 100 No Additional Materials are required. ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024 [Turn over

2 READ THESE INSTRUCTIONS FIRST Write your name, civics group and registration number on all the work you hand in. 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 paper clips, highlighters, 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 and 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. This document consists of 35 printed pages and 1 blank page. ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024

3 Data ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024 [Turn over speed of light in free space, c = 3.00 × 10 8 m s –1 permeability of free space, μ o = 4 π × 10 –7 H m –1 permittivity of free space, ε o = 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

4 Formulae uniformly accelerated motion, s = ut + ½ at 2 v 2 = u 2 + 2 as 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 = work done on/by a gas, W = p Δ V hydrostatic pressure, p = ρ gh gravitational potential, φ = Kepler’s third law of planetary motion T 2 = temperature, T/K = T / o C + 273.15 pressure of an ideal gas, p = mean translational kinetic energy of an ideal gas molecule E = displacement of particle in s.h.m. x = x o sin ω t velocity of particle in s.h.m. v = v o cos ω t = electric current, I = Anvq resistors in series, R = R 1 + R 2 + … resistors in parallel, 1/ R = 1/ R 1 + 1/ R 2 + … ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024

5 capacitors in series 1/ C = 1/ C 1 + 1/ C 2 + … capacitors in parallel C = C 1 + C 2 + … 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 = x o sin ω t 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 = energy in an inductor U = RL series circuits τ = RLC series circuits (underdamped) ω = radioactive decay, x = x o exp (–λ t) decay constant λ = ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024 [Turn over

6 ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024

7 Section A Answer all questions in this section. You are advised to spend about 1 hour 50 minutes on this section. 1 A frictionless hoop of mass M and radius R stands vertically on the ground. Two beads, both of mass m , are released at the same time from rest from the top of the hoop. They slide down the hoop, as shown in Fig. 1.1, where θ is the angular position of the left bead from the vertical direction. (a) Derive an expression of the speed of the beads in terms of θ . [1] (b) Show that, for any angle θ with the normal force acting on the beads by the hoop is towards the centre of the loop. [3] ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024 [Turn over

8 (c) The hoop is not fixed to the ground but is free to move upwards if a large enough force acts on it. Determine the maximum ratio between m and M , such that the hoop will not be lifted off the ground as the two beads slide down. maximum = [6] ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024

9 (d) The hoop is now fixed in position, and one of the beads is removed from the hoop. The remaining bead is displaced from the bottom of the hoop by a small angular displacement φ and then released, as shown in Fig. 1.2. Show that the subsequent motion of the bead is simple harmonic. [3] [Total: 13] ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024 [Turn over

10 2 (a) Fig 2.1 shows a rigid uniform beam AOB of mass M. O is the mid-point of the beam. The beam rests on three vertical springs each having the same unstretched length, but with different spring constants k, 2k and 4 k at A , O and B respectively, k being a constant. The bases of the springs are fixed to a horizontal platform. Determine the compression of each spring in terms of M , k and g . compression of A =……………..…………. compression of O = ….................………... compression of B = ……………………. [6] ©EJC NYJC 2024 9814/J2H3 Preliminary Examination/2024