2024 HCI H3 Prelim P1 QP

This document consists of 33 printed pages and 1 blank page. 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 16 September 2024 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 8 2 7 3 8 4 6 5 14 6 17 Section B 7 20 8 20 9 20 Deductions Total 100

2 © Hwa Chong Institution 9814 H3 Physics / Prelim 2024 Data speed of light in free space c = 3.00  108 m s-1 permeability of free space 0 = 4  10-7 H m-1 permittivity of free space 0 = 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 AN = 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 = 21 2ut at+ v2 = 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 2 T = 234 a GM  temperature T / K = T / °C + 273.15

3 © Hwa Chong Institution 9814 H3 Physics / Prelim 2024 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 = R1 + R2 + …… resistors in parallel 1/R = 1/R1 + 1/R2 + …… capacitors in series 1/C = 1/C1 + 1/C2 + …… capacitors in parallel C = C1 + C2 + …… 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 = ( )expoxt − decay constant  = 1/2 ln2 t

4 © Hwa Chong Institution 9814 H3 Physics / Prelim 2024 Section A Answer all questions in this section. You are advised to spend about 1 hour 50 minutes on this section. 1 (a) The ceiling fan in Fig. 1.1 has blades that are 0.60 m long and is spinning at 80 revolutions in one minute. It is turned off and comes to rest in 40 s. Fig. 1.1 (i) Calculate the speed of the tip of any blade just before the fan is switched off. speed = …………… m s-1 [2] (ii) After it is switched off, determine the fan’s average angular acceleration. average angular acceleration = …………….. rad s-2 [1] (iii) Calculate the number of revolutions that the fan completes before coming to rest. no. of revolutions = …………………….. [2]

5 © Hwa Chong Institution 9814 H3 Physics / Prelim 2024 (b) A uniform solid cylinder of mass M, initially at rest, is mounted on a fixed horizontal axle running through its centre of mass. A small piece of blu-tac, with mass m and velocity v, is projected towards the cylinder, as shown in Fig. 1.2. The line of motion of the projectile is perpendicular to the axle and at a distance of d from the centre, where d < R. Fig. 1.2 Determine the angular speed  , of the system just after the blu-tac sticks to the surface of the cylinder in terms of M, m, v, R and d. [3] [Total: 8 marks] v d R

6 © Hwa Chong Institution 9814 H3 Physics / Prelim 2024 2 (a) Two identical particles of mass m collide elastically on a low -friction table as shown in Fig. 2.1. Show that the total kinetic energy of the system (Ek) after the collision is 21 4 mu in the zero - momentum frame (centre-of-mass frame). [2] (b) Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow, and move off in different directions, as shown in Fig. 2.2. Asteroid A, which was initially traveling at 40.0 m s-1, is deflected 30° from its original direction. Asteroid B, which was initially at rest, travels at 45° to the original direction of A. Fig. 2.2 u m m Fig. 2.1 at rest

7 © Hwa Chong Institution 9814 H3 Physics / Prelim 2024 (i) Calculate the speed of each asteroid after the collision. vA = ……………….. m s-1 vB = ……………….. m s-1 [3] (ii) Determine the fraction of the kinetic energy of asteroid A dissipated during this collision. fraction = ………………….. [2] [Total: 7 marks]

8 © Hwa Chong Institution 9814 H3 Physics / Prelim 2024 3 (a) Fig. 3.1 shows point sources of waves, S1 and S2. P is a point equidistant from the two sources. Fig. 3.1 The sources radiate waves of the same wavelength, but of amplitudes A1 and A2 respectively. At P, the time variation of the disturbance due to the wave from S1 may be represented by y1 = A1 cos  t (i) There is a phase angle  between the waves from the two sources reaching P. Write down an expression for the disturbance y2 due to the wave from S2. [1] (ii) Show that the amplitude of the resultant disturbance, Ar at P is given by 2 2 2 r 1 2 1 2 2 cosA A A A A = + +