NYJC 2026 Timed Practice

1 NANYANG JUNIOR COLLEGE JC2 Timed Practice 2026 General Certificate of Education Advanced Level Higher 3 CANDIDATE NAME CIVICS GROUP - REGISTRATION NUMBER PHYSICS Paper 1 9814/01 09 July 2026 1 hour 30 min Candidates answer on the Question Paper. No Additional Materials are required. 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. Answer all questions. This document consists of 14 printed pages For Examiner’s Use 1 10 2 12 3 10 4 20 Total 52

2 Data Formulae uniformly accelerated motion s = ut + ½at2 work done on/by a gas W = p V v2 = u2 + 2as Pressure p = F A moment of inertia of rod through one end I = ML21 3 gravitational potential  = Gm r− moment of inertia of hollow cylinder through axis I = M r r22 12 1 ()2 + temperature T/K = T / oC + 273.15 moment of inertia of solid sphere through centre I = MR22 5 pressure of an ideal gas p = 21 3 Nm cV moment of inertia of hollow sphere through centre I = MR22 3 mean translational kinetic energy of an ideal gas particle E = 3 2 kT speed of light in free space, c = 3.00  108 m s–1 permeability of free space, μo = 4π  10–7 H m–1 permittivity of free space, εo = 8.85  10–12 F m–1 ( . −= 91 0 1 8 99 10 m F4 ) 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

3 displacement of particle in s.h.m. x = xo sin ωt alternating current/voltage, x = xo sin ωt velocity of particle in s.h.m. v = vo cos ωt magnetic flux density due to a long straight wire B = 2 o d   I = ( )22 xxo − magnetic flux density due to a flat circular coil B = 2 oN r  I electric current, I = Anvq magnetic flux density due to a long solenoid B = on I resistors in series, R = R1 + R2 + … energy in an inductor U = L 21 2 I resistors in parallel, R 1 = RR12 11 ...++ RL series circuits 𝜏 = L R capacitors in series C 1 = CC12 11 ...++ RLC series circuits (underdamped) ω = R LC L − 2 2 1 4 capacitors in parallel C = C1 + C2 + … energy states for quantum particle in a box nE = h nmL 2 2 28 energy in a capacitor U = QV1 2 radioactive decay x0 = txe0 − = Q C 21 2 radioactive decay constant  = t1/2 ln2 = CV 21 2 Lorentz factor  = v c 2 1 1 − charging a capacitor Q = t Qe0 1 −−  length contraction L = L0  discharging a capacitor Q = t Qe0 − time dilation T = T0 RC time constant  = RC Lorentz transformation equations (1 dimension) x ' = ( )x vt − electric potential, V = 4 o Q r t ' = vxt c2  − electric field strength due to a long straight wire E = or  2 velocity addition u' = uv uv c2 () 1 −  − electric field strength due to a large sheet E = o  2 mass-energy equivalence E 2 = pc mc2 2 2( ) ( ) +

4 Answer all questions. 1 Two perfectly elastic balls, A and B, are held above the ground at a height h, such that h is much greater than the diameter of each ball. The balls are almost touching, with ball A directly above ball B. The balls are released simultaneously. Ball A rebounds to a maximum height H above the ground. (a) Sketch a labelled diagram to show the velocities of the balls relative to the ground just before they collide with each other. Hence show that when the balls collide with each other, they do so with relative velocity relv gh= 8 [3] (b) The mass of the lower ball mB is greater than or equal to the mass of the upper ball mA so that: B A m nnm = and 1 Determine an expression for the velocity of the centre of mass frame vCoM relative to the ground immediately before the two balls collide. [2]

5 (c) (i) Determine an expression for the ratio of the rebound height H to the drop height h. [3] (ii) Deduce the maximum value of H h for n 1 . maximum value of H h =………………………………. [2] [Total: 10]

6 2 A consequence of special relativity is that observers in different inertial reference frames disagree on the lengths of objects and the times between events. (a) State what is meant by an inertial observer. ………………………………………………………………………………………………………. …………………………………………………………………………………………………… [1] (b) An inertial reference frame (x, y, z, t) has Earth as its origin. Ignore the rotational motion of Earth as negligible on the length scale of interest. In this reference frame, the star Proxima Centauri is a distance of 4.25 light years (ly) along the positive x-axis, as shown in Figure 2.1. Figure. 2.1 A spacecraft leaves Earth at t = 0 and travels directly to Proxima Centauri at a speed of c 2 . Assume that there is negligible relative motion between Earth and Proxima Centauri. The origin of an inertial reference frame (x ', y ', z ', t ' ) moving with the spacecraft coincides with the origin of the Earth’s reference frame at the moment the spacecraft leaves the Earth.

7 (i) Write down the x and t coordinates of the spacecraft in Earth’s reference frame at the moment of departure from Earth and at the moment of arrival at Proxima Centauri. Use units of light years (ly) for x and years (yr) for t. In these units, c = 1. x at departure = ……………………………. ly t at departure = ……………………………. yr x at arrival = ……………………………. ly t at arrival = ……………………………. yr [3] (ii) Use the Lorentz transformation equations to write down the x ' and t ' coordinates of the spacecraft at the moment of departure from Earth and at the moment of arrival at Proxima Centauri. Use units of light years (ly) for x ' and years (yr) for t '. In these units, c = 1. x’ at departure = ……………………………. ly t’ at departure = ……………………………. yr x’ at arrival = ……………………………. ly t’ at arrival = ……………………………. yr [4]

8 (iii) Using your answer in 2(b)(ii) or otherwise, calculate the distance from Earth to Proxima Centauri in the (x ', y ', z ', t ' ) frame. distance = ……………………………. ly [1] (iv) The spacecraft returns immediately to Earth at the same speed of c 2 . Explain why, for an inertial observer onboard the spacecraft, this journey could be considered a form of time travel. Support your explanation with calculations. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. [3] [Total: 12]

9 3 Fig. 3.1 shows a side view and top view of a helicopter hovering stationary in mid-air. The two rotor blades of the helicopter can be modelled as uniform thin rectangular plates of length R and width c, as shown in Fig. 3.2. y Fig. 3.2 (not to scale) The gap between the two rotor blades is negligible when compared with the total length of the blades. (a) Show, from first principles, that the moment of inertia, I, of the rotor blades about the x-axis in Fig. 3.2 is given by I = 21 12 Mc where M is the total mass of the rotor bl