2023 RI H2 Physics Prelims P3 Section A Questions

Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2023 Preliminary Examination PHYSICS Higher 2 Paper 3 Longer Structured Questions 9749/03 September 2023 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your index number, name and class 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 or graphs. 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. Section B Answer one question only and circle the question number on the cover page. You are advised to spend one and a half hours on Section A and half an hour on Section B. The number of marks is given in brackets [ ] at the end of each question or part question. *This booklet only contains Section A. For Examiner’s Use Section A 1 / 9 2 / 10 3 / 8 4 / 10 5 / 7 6 / 8 7 / 8 Section B (circle question attempted) 8 / 20 9 / 20 Deduction Total / 80 This document consists of 16 printed pages.

2 © Raffles Institution Data speed of light in free space c = 81 3.00 10 m s −  permeability of free space 0 = 71 4 10 H m −−  permittivity of free space 0 = 12 1 8.85 10 F m −−  ( )( ) 91 1 36 10 F m −−  elementary charge e = 19 1.60 10 C −  the Planck constant h = 34 6.63 10 J s −  unified atomic mass constant u = 27 1.66 10 kg −  rest mass of electron me = 31 9.11 10 kg −  rest mass of proton mp = 27 1.67 10 kg −  molar gas constant R = 1 18.31 J K mol − − the Avogadro constant NA = 23 16.02 10 mol − the Boltzmann constant k = 23 11.38 10 J K − − gravitational constant G = 11 226.67 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+ work done on / by a gas W = pV hydrostatic pressure p = ρgh gravitational potential  = Gm r− temperature T / K = / C 273.15T + 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 = 1/R1 + 1/R2 + …. electric potential V = 4 Q r  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 radioactive decay x = ( )0 expxt − decay constant  = 1/2 ln2 t

3 © Raffles Institution [Turn over Section A Answer all the questions in the spaces provided. 1 (a) The angular velocity  of a satellite in a circular orbit of radius r about the Earth is given by: kAr = where A and k are constants. (i) Use Newton's law of gravitation to write an equation that relates the centripetal force on the satellite to the gravitational force acting on the satellite and determine the value of k. k = [2] (ii) A geostationary orbit has a radius of 42 000 km. Determine the angular velocity of a satellite with an orbital radius of 6700 km. angular velocity = rad s−1 [2] (b) (i) By considering the potential energy and kinetic energy of the satellite, show that the total energy ET of the satellite in a circular orbit of radius r about the Earth is given by: T 2 GMmE r=− where M and m are the masses of the Earth and the satellite respectively. [2]

4 © Raffles Institution (ii) When a geostationary satellite is near the end of its useful life, it will be decommissioned and moved to a graveyard orbit. A graveyard orbit is an orbit that lies far away from common orbits used by satellites in service and it s radius is at least 300 km more than that of the geostationary orbit. The mass of the Earth is 6.0  1024 kg. Determine the minimum energy needed to bring a geostationary satellite of mass 700 kg to a graveyard orbit from a geostationary orbit. minimum energy = J [2] (c) The Moon is the Earth’s only natural satellite. Its orbital path is actually elliptical and not circular. Fig. 1.1 shows the orbit of the Moon about the Earth when viewed normal to the plane of the orbit of the Moon. There are points where the Moon is closer to the Earth and points when it is further from the Earth. Fig. 1.1 (not to scale) On Fig. 1.1, mark with a cross on the Moon’s orbit where the Moon has the largest speed. Explain your answer. [1] Moon’s orbit Earth

5 © Raffles Institution [Turn over 2 In a particular combustion engine, a fixed amount of ideal gas undergoes a cycle of four stages as shown in Fig. 2.1. Fig. 2.1 Some values for the pressure p and volume V of the gas at the various states are labelled in the figure. The four stages of the cycle are: A → B: the gas gains 2625 J of heat through an explosion and the pressure rises rapidly before decreasing to 7.0  105 Pa at state B B → C: the gas expands to state C C → D: the gas cools to state D at constant volume D → A: the gas is compressed at constant temperature to state A. (a) The temperatures of the gas at states B and C are 1260 K and 960 K respectively. (i) Determine the pressure of the gas at state C. pressure = Pa [2] p / 105 Pa V / 10−3 m3 A B (1260 K) C (960 K) D 7.0 1.5 4.0 1.0 4.0 1.0

6 © Raffles Institution (ii) Hence, determine the magnitude of the work done by the gas in the stage B → C. work done = J [2] (b) The stage D → A is compression at constant temperature. State two conditions under which the process in the engine is carried out such that it may be considered to be a constant temperature process. 1. 2. [2] (c) Some energy changes during one cycle of the engine are shown in Fig. 2.2. Complete Fig. 2.2. stage work done on gas / J heat supplied to gas / J increase in internal energy / J A → B −1000 2625 B → C 500 C → D D → A −555 Fig. 2.2 [3] (d) In Fig. 2.1, the stage A → B is represented by a curve. Explain why it may not be appropriate to represent the process with a curve on the graph. [1]

7 © Raffles Institution [Turn over 3 Fig. 3.1 shows two slits S 1 and S2, separated by distance a, illuminated by a point source of light producing coherent light of wavelength 750 nm. The light source is equidistant from both slits. Fig. 3.1 (not to scale) A light detector, 2.00 m below the slits, is moving to the right at a uniform speed v, in the direction shown. (a) When the detector is directly below S1, the detector records a minimum intensity reading. Show that the minimum value for a is 1.22 mm. [2] (b) The slits are now fixed at 1.22 mm apart, with the light source still equidistant from both slits. (i) The detector detects three maxima per second while moving to the right. Determine the speed v at which the detector is moving. v = m s–1 [2] light source detector 2.00 m path of detector