2021 HCI H3 Physics Prelim 2021 Question Paper

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 2021 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 7 3 12 4 9 5 9 6 16 Section B 7 20 8 20 9 20 Deductions Total 100

2 © Hwa Chong Institution 9814 H3 Physics / Prelim 2021 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 2021 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 2021 Section A Answer all questions in this section. You are advised to spend about 1 hour 50 minutes on this section. 1 An ideal gas confined in a cylinder is put through a closed cycle. Initially the gas is at state A where it has pressure Po, volume Vo, and temperature To. First, its pressure is tripled under constant volume. It then expands at constant temperature to its original pressure and finally it is compressed at constant pressure to its original volume. The P-V diagram of the cyclic process is shown in Fig. 1. (a) Determine an expression for the temperature of the gas at state C, in terms of T0. [1] (b) Show that the net work done by the gas in one complete cycle is  0 3ln3 2nRT  . [3] P V Po Vo 3Po 3V0 B C A Fig. 1

5 © Hwa Chong Institution 9814 H3 Physics / Prelim 2021 (c) Explain for each process below whether heat is supplied to the gas. A to B: …...………….……………………………………………………………………………………. ……………………….……………………………………………………………………………………. ……………………….……………………………………………………………………………………. B to C: …...………….……………………………………………………………………………………. ……………………….……………………………………………………………………………………. ……………………….……………………………………………………………………………………. ……………………….……………………………………………………………………………………. C to A: …...………….……………………………………………………………………………………. …………………………….………………………………………………………………………………. …………………………….………………………………………………………………………………. …………………………………..…………………………………………………………………...… [3] [Total: 7]

6 © Hwa Chong Institution 9814 H3 Physics / Prelim 2021 2 (a) A block of mass m is connected to two springs which have spring constants of 1k and 2k , respectively, as shown in Fig. 2.1. Fig. 2.1 The block moves on a frictionless table after it is displaced from equilibrium and released. It performs simple harmonic motion. Show that the period of the block is  12 12 2 m k kT kk  [4] m frictionless table

7 © Hwa Chong Institution 9814 H3 Physics / Prelim 2021 (b) Three objects of uniform density – a hollow cylinder (A), a solid cylinder (B) and a solid sphere (C) – are placed at the top of an incline as shown in Fig. 2.2. Fig. 2.2 They are released at the same elevation and roll without slipping. Considering the fact that the outcome is independent of the masses and the radii of the objects, explain which object reaches to the bottom first. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. ………………………………………………………………………………………………………… [3] [Total: 7] bottom top

8 © Hwa Chong Institution 9814 H3 Physics / Prelim 2021 3 (a) Our Sun is one of the approximately 10 11 stars in our host galaxy, the Milky Way. There is a supermassive black hole at the ce