HCI 2022 Prelim P2

This document consists of 25 printed pages. HWA CHONG INSTITUTION JC2 Preliminary Examination Higher 2 CANDIDATE NAME CT GROUP 21S CENTRE NUMBER INDEX NUMBER PHYSICS Paper 2 Structured Questions Candidates answer on the Question Paper. No Additional Materials are required. 9749/02 13 September 2022 2 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 a soft pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. The number of marks is given in brackets [ ] at the end of each question or part question. You are reminded of the need for good English and clear presentation in your answers. For Examiner’s Use Paper 2 1 11 2 8 3 10 4 8 5 10 6 11 7 22 Deductions Total 80

2 © Hwa Chong Institution 2022 9749 / JC2 Preliminary Examination Data Formulae speed of light in free space, c = 3.00  10 8 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  10 23 mol -1 the Boltzmann constant, k = 1.38  10 -23 J K -1 gravitational constant, G = 6.67  10 -11 N m 2 kg -2 acceleration of free fall, g = 9.81 m s -2 uniformly accelerated motion work done on / by a gas hydrostatic pressure gravitational potential temperature pressure of an ideal gas mean kinetic energy of a molecule of an ideal gas displacement of particle in s.h.m. velocity of particle in s.h.m. electric current resistors in series resistors in parallel electric potential alternating current / voltage magnetic flux density due to a long straight wire magnetic flux density due to a flat circular coil magnetic flux density due to a long solenoid radioactive decay decay constant s = ut + 2 1 at2 v 2 = u 2 + 2as W = p V p = gh r Gm−= T/K = T/ C + 273.15 P = 21 3 Nm cV  kTE 2 3= x = xo sin t v = vo cos t = )( 22 xxo − I = Anvq R = R1 + R2 + . . . 1/R = 1/R1 + 1/R2 + . . . r QV o4= x = xo sin  t 2 oμB d=  I 2 oμNB r= I B = onI x = xo exp ( -t ) 1 2 ln2 t =

3 © Hwa Chong Institution 2022 9749 / JC2 Preliminary Examination 1 (a) A student uses the following setup in Fig. 1.1 to find the spring constant k of a spring. Fig. 1.1 The student obtained the following results from his experiment: Length of spring when no mass is added: L1 = (1.3 ± 0.1) cm Length of spring when mass M is added: L2 = (3.7 ± 0.2) cm Mass of M = (98.5 ± 0.2) g You may assume that the elastic limit of the spring has not been exceeded in his experiment. (i) Show that the spring constant k of the spring is 40.3 N m-1. [2] (ii) Calculate the actual uncertainty in k. actual uncertainty in k = N m-1 [2] (iii) State the value of k and its actual uncertainty to the appropriate precision. k = ( ± ) N m-1 [1]

4 © Hwa Chong Institution 2022 9749 / JC2 Preliminary Examination (b) Fig. 1.2 shows a wooden cube P of volume V floating on the surface of a liquid with density . 30% of the volume of the cube is above the surface of the liquid. Fig. 1.2 The top face of cube P is now connected to a light string, which passes over a smooth pulley and supports an identical cube Q at its other end, which rests on a smooth inclined plane at an angle θ to the horizontal, as shown in Fig 1.3. Fig. 1.3 At its new equilibrium position, 60% of the volume of Cube P is now above the surface of the liquid. (i) On Fig. 1.4, label clearly all forces acting on Cube P when it is at its new equilibrium position. Fig. 1.4 [2] pulley

5 © Hwa Chong Institution 2022 9749 / JC2 Preliminary Examination (ii) State the expression for the weight W of cube P in terms of V and  . [1] (iii) Hence, show that the tension in the string is 3 7 W . [2] (iv) Determine the value of θ.  =  [1] [Total :11]

6 © Hwa Chong Institution 2022 9749 / JC2 Preliminary Examination 2 Jupiter has close to eighty moons, of which eight of them are in approximately circular orbits. Jupiter has a mass MJ, radius RJ and a Jupiter-day is approximately 0.417 Earth-days. The orbital radii and periods of two of the moons of Jupiter are tabulated in Fig. 2.1. The orbital radii and the orbital periods of these moons are expressed in units of RJ and Earth-days respectively. Name of Moon Orbital Radius / RJ Orbital Period / Earth-days Amalthea 2.62 Thebe 3.18 0.676 Fig. 2.1 (a) (i) Show that the period T of a circular orbit around Jupiter, expressed in terms of the radius of the orbit R is given by 234 J RT GM = [2] (ii) Using the data provided in Fig 2.1, complete Fig. 2.1 with the orbital period for Amalthea. Show all working in the space below. orbital period = Earth-days [2]

7 © Hwa Chong Institution 2022 9749 / JC2 Preliminary Examination (b) (i) Determine an expression for the orbital speed v of a moon in terms of its orbital radius R and any other constants. [1] (ii) It is suggested that Jupiter’s rings are formed from material ejected from the moons as the moons collide with meteorites. Assuming no change in the speed of a moon, explain whether the moon can stay in orbit if it experiences a constant loss of mass. [1] (c) Using the data available for the moons of Jupiter, a graph of the orbital period was plotted against the orbital radius as shown in Fig 2.2. (i) A satellite is moving in a “geostationary orbit” about Jupiter i.e. it is in an orbit above the same geographical spot on Jupiter. Using Fig . 2.2, estimate the radius of this “geostationary orbit”. radius = RJ [1] (ii) Suggest a possible use for this “geostationary satellite” in (c)(i). [1] [Total: 8] 0.0 0.5 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Orbital Period /Earth-days Orbital Radius / RJ Fig. 2.2

8 © Hwa Chong Institution 2022 9749 / JC2 Preliminary Examination 3 A sound wave that is propagating towards the left is represented by the two graphs below. Fig. 3.1 shows the variation with position along the wave of the displacement of the air particles from their equilibrium position at time t = 0. Fig. 3.2 shows the variation with time t of the displacement of an air particle from its equilibrium position. (a) Calculate the speed of the sound wave. speed = m s-1 [2] (b) Fig. 3.1 shows three particles P, Q and R along the sound wave. Taking rightwards to be positive, identify the particle that is (i) instantaneously at rest at t = 0. particle : [1] (ii) at the centre of a rarefaction at t = 0. pa