2023 HCI H3 Prelim P1 QP

This document consists of 30 printed pages. HWA CHONG INSTITUTION JC2 Preliminary Examination Higher 3 CANDIDATE NAME CENTRE NUMBER INDEX NUMBER PHYSICS Paper 1 Candidates answer on the Question Paper. No Additional Materials are required. 9814/01 21 September 2023 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. 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. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use Section A 1 7 2 9 3 11 4 8 5 6 6 19 Section B 7 20 8 20 9 20 Deductions Total 100

2 © Hwa Chong Institution 9814 H3 Physics / Prelim 2023 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 −− −−   elementary charge e = 191.60 10 C− the 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−− the Avogadro constant AN = 23 16.02 10 mol − the 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 s = 21 2ut at+ 2v = 2 2u as+ 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 = pV hydrostatic pressure p = gh gravitational potential  = /Gm r− Kepler’s third law of planetary motion 2T = 234 a GM  temperature /KT = / C 273.15T +

3 © Hwa Chong Institution 9814 H3 Physics / Prelim 2023 pressure of an ideal gas p = 21 3 Nm cV mean translational kinetic energy of an ideal gas molecule E = 3 2 kT displacement of particle in s.h.m. x = 0 sinxt  velocity of particle in s.h.m. v = 0 cosvt  = ( ) 22 0xx− electric current I = Anvq resistors in series R = 12 ...RR++ resistors in parallel 1/ R = 121/ 1/ ...RR++ capacitors in series 1/ C = 121/ 1/ ...CC++ capacitors in parallel C = 12 ...CC++ energy in a capacitor U = 21 2CV electric potential V = 04 Q r electric field strength due to a long straight wire E = 02 r   electric field strength due to a large sheet E = 02   alternating current/voltage x = 0 sinxt  magnetic flux density due to a long straight wire B = 0 2 d   I magnetic flux density due to a flat circular coil B = 0 2 N r  I magnetic flux density due to a long solenoid B = 0n I energy in an inductor U = 21 2 LI RL series circuits  = L R RLC series circuits (underdamped)  = 2 2 1 4 R LC L− radioactive decay x = ( )0 expxt − decay constant  = 1/2 ln2 t

4 © Hwa Chong Institution 9814 H3 Physics / Prelim 2023 Section A Answer all questions in this section. You are advised to spend about 1 hour 50 minutes on this section. 1 (a) Explain what is meant by an inertial reference frame. ………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………. …………………………………………………………………………………………………………… [2] (b) Two identical carts A and B move toward each other on a low-friction track. The speed of cart A is 2u, while the speed of cart B is 3u in the Earth reference frame. The system of the two carts has kinetic energy K. State and explain another inertial frame of reference in which the kinetic energy of the two-cart system has the same kinetic energy K. ……………………………………………………………………………………………………………..... ………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………. ………………………………………………………………………………………………………..… [2] (c) An object of mass m moving with a speed of u strikes a stationary object that has mass 0.5m. Determine the fraction of the initial kinetic energy of the system that is convertible to internal energy of the system. [3] [Total: 7]

5 © Hwa Chong Institution 9814 H3 Physics / Prelim 2023 2 A uniform solid reel of mass 2M is made of three discs of equal thickness d, the outer two being of radius 2R and the middle one of radius R, fixed together so that the discs have a common axis. Front View Side View Fig. 2.1 (a) (i) Express the density of the reel in terms of M, R and d. [1] (ii) Hence, show that the moment of inertia I of the reel about its axis is given by 211 3 MR=I . [3] axis d R 2R d d

6 © Hwa Chong Institution 9814 H3 Physics / Prelim 2023 (b) A light inextensible string, wound several times around the rough central disc of the reel, passes over a fixed smooth peg at B and carries a box of mass M at its free end. The reel stands on a rough plane inclined at 30 to the horizontal. The straight portion of the string from B to the reel is parallel to the slope of the plane and the portion BC is vertical. The box falls vertically with the string taut, and the reel, whose axis is horizontal, rolls up the inclined plane without slipping. Find an expression for the acceleration of the box in terms of the acceleration of free fall, g. Fig. 2.2 [5] [Total: 9] 30 B M C

7 © Hwa Chong Institution 9814 H3 Physics / Prelim 2023 3 (a) State Kepler’s first law of planetary motion. ………………………………………………………………………………………………………….…… …………………………………………………………………………………………………………… [1] (b) A rocket is to be fired from Earth, to reach Venus by means of a Hohmann transfer orbit. While in the transfer orbit, the only force on the rocket will be the gravitational force due to the Sun. (i) On Fig. 3.1, draw and label the transfer orbit from Earth to Venus.