DHS 2026 H3 Physics Prelim

© DHS 2026 9814/01 Name: Index Number: Class: DUNMAN HIGH SCHOOL Preliminary Examination Year 6 H3 PHYSICS Paper 1 Structured Questions 9814/01 28 September 2026 3 hours You must answer on the question paper. No additional materials are needed. READ THESE INSTRUCTIONS FIRST Write your class, index number and name in the spaces at the top of this page. Use a dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams, graphs or rough working. 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. Section A Answer all questions. You are advised to spend 1 hour and 50 minutes on Section A. Section B Answer two questions only. You are advised to spend 35 minutes on each question in Section B. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 32 printed pages. Any blank pages are indicated. For Examiner’s Use Section A 1 7 2 8 3 10 4 8 5 12 6 15 Section B 7 20 8 20 9 20 s.f -1 Total 100

2 © DHS 2026 9814/01 Data speed of light in free space, c = 3.00 × 108 m s−1 permeability of free space, o = 4 × 10−7 H m−1 permittivity of free space, o = 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, 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 = ut + 1 2 at2 v2 = u2 + 2as moment of inertia of rod through one end I = 21 3 ML moment of inertia of hollow cylinder through axis I = ( ) 22 12 1 2 M r r + moment of inertia of solid sphere through centre I = 22 5 MR moment of inertia of hollow sphere through centre I = 22 3 MR work done on/by a gas W = pV pressure p = F A gravitational potential  = GM r−

3 © DHS 2026 9814/01 [Turn over temperature T/K = T/oC + 273.15 pressure of an ideal gas p = 21 3 Nm cV  mean translational kinetic energy of an ideal gas molecule E = kT23 displacement of particle in s.h.m. x = x0 sin t velocity of particle in s.h.m. v = v0 cos t =  22 xxo − electric current I = nAvq resistors in series R = R1 + R2 + … resistors in parallel 1 R = 12 11 RR++  capacitors in series 1 C = 12 11 CC++  capacitors in parallel C = C1 + C2 + … energy in a capacitor U = 1 2QV = 21 2 Q C = 21 2CV charging a capacitor Q = 0 1 t Qe −−  discharging a capacitor Q = 0 t Qe − RC time constant  = RC electric potential V = r Q o4 electric field strength due to a long straight wire E = 02 r   electric field strength due to a large sheet E = 02  

4 © DHS 2026 9814/01 alternating current / voltage x = x0 sin t magnetic flux density due to a long straight wire B = 0 2 d I  magnetic flux denxity due to a flat circular coil B = 0 2 N r I magnetic flux density due to a long solenoid B = 0nI energy in an inductor U = 21 2 LI RL series circuits  = L R RLC series circuits (underdamped)  = 2 2 1 4 R LC L− energy states for quantum particle in a box nE = 2 2 28 h nmL radioactive decay x = x0 exp(−t) radioactive decay constant  = 1 2 ln2 t Lorentz factor  = 2 1 1 vc− length contraction L = 0L  time dilation T = 0T Lorentz transformation equations (1 dimension) 'x = ( )x vt − 't = 2 vxt c − velocity addition 'u = 21 uv uv c − − relativistic energy-momentum relation 2E = ( ) ( ) 22 2pc mc+

5 © DHS 2026 9814/01 [Turn over 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 range R of the projectile launched from a slope with an initial speed u at an angle θ above the horizontal. The slope is of constant gradient and makes an angle  with the horizontal. Fig. 1.1 (a) State an expression for the time-of-flight t of the projectile in terms of R, u and θ. [1] (b) State an expression for the vertical displacement h of the projectile in terms of R and  . [1]

6 © DHS 2026 9814/01 (c) By using your expressions in (a) and (b) or otherwise, show that the general range equation takes the form: ( ) 2 sin2 1 cos2 tanuR g   = + + . Hint: You may find it useful to use the trigonometric identity: 22cos 1 cos2xx=+ . [3] (d) For a given value of  , determine the relationship between θ and  that maximises the range. Hint: You may find it helpful to use one of the trigonometric identities: 2 2 1sin cos sin tan 1 tantan 2 ba x b x a b x a xx  −+ = + +  =−  [2] [Total: 7]

7 © DHS 2026 9814/01 [Turn over 2 Two spherical masses of mass m1 = 100 g and m2 = 300 g are suspended from point A by two equal inextensible strings, each of length The mass m1 is drawn aside and held at the same level as A but at a distance of 0.5 L from A as shown in Fig 2.1. When ball m1 is released, it collides elastically with the stationary ball m2. Fig. 2.1 (a) Assuming that air resistance is negligible, show that the velocity u1 in which the ball of mass m1 collides with mass m2 is given by the expression: 1 332 4u gL =−  where g is the acceleration of free fall. [3] 0.5 L A

8 © DHS 2026 9814/01 (b) Given that L = 1.0 m and assuming that the diameters of the masses are negligible compared to L. (i) Calculate the magnitude of the velocity ZMFv of the zero momentum frame for the collision between m1 and m2. magnitude of ZMFv = ………………………… m s−1 [2] (ii) Hence, determine the maximum height reached by mass m2 after the collision. maximum height = ………………………… m [3] [Total: 8]

9 © DHS 2026 9814/01 [Turn over 3 A light string is coiled around the spool. As shown in Fig. 3.1, the spool comprises of two thin discs of radius R and mass M, and a solid cylindrical centre of radius r0 and mass m. All components of the spool have uniform mass distribution. Fig. 3.1 The frictional force from the ground is sufficient such that the spool does not slip. (a) Using calculus, derive the moment of inertia of the solid cylinder in the spool with axis of rotation through its minimum inertia axis as shown in Fig. 3.2. Fig. 3.2 [3]

10 © DHS 2026 9814/01 (b) Derive an expression for the acceleration of the centre of mass in terms of F, R, r0, M and m. [3] (c) Derive an expression for the frictional force f between the spool and the ground and state its direction. f = ………………………………. N direction = ……………………… [3] (d) The string is now pulled at a different angle with a force F1 and the spool does not roll or slip. On Fig. 3.1, draw the vector of the force F1 and its line of action. [1] [Total: 10]