CJC.2025.H2.Phy.PRELIM.P3.Ans

CANDIDATE NAME MARK SCHEME CLASS 2T PHYSICS 9749/03 Paper 3 Longer Structured Questions September 2025 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your 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, 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. Answer all questions. Section A Answer all questions. Section B Answer one question only. 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 document consists of 32 printed pages and 0 blank page. [Turn over FOR EXAMINER’S USE SECTION A Q1 / 8 Q2 / 8 Q3 / 11 Q4 / 6 Q5 / 10 Q6 / 7 Q7 / 10 SECTION B Q8 / 20 Q9 / 20 PAPER 3 / 80 PAPER 2 / 80 PAPER 1 / 30 PAPER 4 / 55 TOTAL (WEIGHTED) % Catholic Junior College JC2 Preliminary Examinations Higher 2

2 DATA speed of light in free space c = 3.00 x 108 m s-1 permeability of free space 0 = 4 x 10-7 H m-1 permittivity of free space 0 = 8.85 x 10-12 F m-1 (1/(36)) x 10-9 F m-1 elementary charge e = 1.60 x 10-19 C the Planck constant h = 6.63 x 10-34 J s unified atomic mass constant u = 1.66 x 10-27 kg rest mass of electron me = 9.11 x 10-31 kg rest mass of proton mP = 1.67 x 10-27 kg molar gas constant R = 8.31 J K-1 mol-1 the Avogadro constant NA = 6.02 x 1023 mol-1 the Boltzmann constant k = 1.38 x 10-23 mol-1 gravitational constant G = 6.67 x 10-11 N m2 kg-2 acceleration of free fall g = 9.81 m s-2

3 [Turn over FORMULAE uniformly accelerated motion s = u t + ½ a t2 v2 = u2 + 2as work done on / by a gas W = p V hydrostatic pressure p = gh gravitational potential  = - Gm r temperature T / K = T / ˚C + 273.15 pressure of an ideal gas p = 1 3 Nm V 〈c2〉 mean translational kinetic energy of an ideal gas molecule E = 3 2 kT displacement of particle in s.h.m. x = x0 sin t velocity of particle in s.h.m. v = v0 cos t = 22 0 xx − electric current I = Anvq resistors in series R = R1 + R2 + ... resistors in parallel 1/R = 1/R1 + 1/R2 + ... electric potential V = Q 4πεor alternating current / voltage x = x0 sin t magnetic flux density due to a long straight wire B = μoI 2πd magnetic flux density due to a flat circular coil B = μoNI 2r magnetic flux density due to a long solenoid B = μonI radioactive decay x = x0 exp(-t) decay constant λ = 1 2 ln2 t

4 Section A Answer all questions in the spaces provided. 1 A solid iron sphere of density 8000 kg m–3 and volume 4.50  10-4 m3 is completely submerged in a liquid of density 800 kg m–3. The iron sphere is resting on a spring, as shown in Fig. 1.1. The spring is compressed by 10.2 cm. Fig. 1.1 (a) Show that the upthrust on the iron sphere is 3.53 N. [1] Solution Upthrust ( )( ) 4800 4.50 10 9.81 3.5316 N Vg − = = = = 3.53 N (Shown) M1 A0 (b) Hence, calculate the force constant of the spring. force constant = ………….…….……………. N m-1 [2] Solution At equilibrium, considering forces on the iron sphere kx + U = mg ( )( ) −−−== 48000 4.50 10 9.81 3.5316 0.102 mg Uk x = 312 N m-1 M1 A1 iron sphere liquid compressed spring

5 [Turn over [Total: 8] (c) A string of breaking strength 32.0 N is used to lift the iron sphere vertically upwards, as shown in Fig. 1.2. The iron sphere is then lifted partially out of the liquid as shown in Fig. 1.3. Fig. 1.2 Fig. 1.3 (i) Explain why the string breaks as the sphere emerges from the liquid. ……………………………………………………………………………………………... ……………………………………………………………………………………………... ……………………………………………………………………………………………... ..…………………………………………………………………………………….... [2] Solution When the sphere is lifted out of the liquid, the volume of liquid displaced is reduced. This causes the upthrust acting on sphere to decrease. To maintain equilibrium, the tension will increase and the string breaks when the tension exceeds the maximum allowable value. B1 B1 (ii) Calculate the volume of the fluid displaced at the instant when the string breaks. volume = ……….…………...…………… m3 [3] Solution At breaking point, +=T U mg ( )( ) ( ) −+ =  432.0 800 9.81 8000(4.50 10 ) 9.81V V = 4.23  10-4 m3 C1 M1 A1 string

6 2 (a) A satellite S of mass m is in a stable circular orbit at an altitude of 2 R above the surface of a planet of mass M and radius R, as shown in Fig. 2.1. Assume the planet has no atmosphere and that all its mass is concentrated at its centre. Fig. 2.1 (a) Show that the kinetic energy Ek of the satellite S in orbit is given by the expression: Ek= GMm 6R where G is the gravitational constant. [2] Solution: The gravitational force provides the centripetal force. FG = FC GMm (3R)2 = mv2 3R v2 = (3R)Mm (3R)2m = GM 3R KE = 1 2 mv2 = 1 2 m GM 3R = GMm 6R B1 B1 R planet, mass M satellite S, mass m

7 [Turn over (b) The planet has mass 4.5 × 10²⁴ kg and radius of 5.5 × 10 3 km. The satellite has a mass of 1500 kg. Determine the total energy of satellite S in orbit. total energy = ………………………………. J [2] Solution: Total energy = - GMm 2r where r is the orbital radius and is equal to 3R for this Q = (6.67 × 10⁻¹¹)(4.5 × 10²⁴)1500 2 x 3(5.5 × 103x103) = - 1.36 × 1010 J (negative sign to be included) If students equate Ek to ET, there must be some derivation shown to get M1 marks. M1 A1 (c) A second satellite P is launched into orbits from the surface of the same planet with an initial kinetic energy of 2.0 × 10¹⁰ J. It rises to a distance of 4R from the centre of the planet. On the axes provided in Fig 2.2, sketch a graph to show how the satellite’s orbital kinetic energy varies with distance from the centre of the planet as it moves from R to 4R. Fig 2.2 [2]

8 Solution: B1 – Shape of graph: • Smooth curve decreasing with increasing r (concave upwards) 1 mark – Correct key points labelled or plotted: • Correctly labels or plots the following values: Since Ek α 1 r r EK / 1010 J R +2.0 2R +1.0 3R +0.67 4R +0.5 (d) A third satellite Q is to be launched vertically from the surface of the same planet. Determine the minimum speed that satellite Q must be given at the surface to escape the planet’s gravitational field. minimum speed = …………………………… m s-1 [2]

9 [Turn over [Total: 8] Solution: By conservation of energy, Energy of satellite