Cambridge A Level Physics 9702 — 2002 May/June Paper 4 · Variant 1

TIME 1 hour INSTRUCTIONS TO CANDIDATES Write your name, Centre number and candidate number in the spaces at the top of this page. Answer all questions. Write your answers in the spaces provided on the question paper. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. You may lose marks if you do not show your working or if you do not use appropriate units. CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level PHYSICS 9702/4 PAPER 4 MAY/JUNE SESSION 2002 1 hour Candidates answer on the question paper. No additional materials. This question paper consists of 15 printed pages and 1 blank page. SPA (NH/CG) S14609/4 © CIE 2002 [Turn over Candidate Centre Number Number Candidate Name FOR EXAMINER’S USE

2 9702/4 M/J/02 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 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 × 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

3 9702/4 M/J/02 [Turn over Formulae uniformly accelerated motion, s = ut +
 at 2 v2 = u2 + 2as work done on/by a gas, W = pV gravitational potential, φ = – simple harmonic motion, a = –
2x velocity of particle in s.h.m., v = v0 cos
t v = ±
√(x2 0 – x2) resistors in series, R = R1 + R2 + . . . resistors in parallel, 1/R = 1/R1 + 1/R2 + . . . electric potential, V = capacitors in series, 1/C = 1/C1 + 1/C2 + . . . capacitors in parallel, C = C1 + C2 + . . . energy of charged capacitor, W =
 QV alternating current/voltage, x = x0 sin
t hydrostatic pressure, p = qgh pressure of an ideal gas, p =
 <c2> radioactive decay, x = x0 exp(– t) decay constant,  = critical density of matter in the Universe, q0 = equation of continuity, Av = constant Bernoulli equation (simplified), p1 +
 qv2 1 = p2 +
 qv2 2 Stokes’ law, F = Arv Reynolds’ number, Re = drag force in turbulent flow, F = Br2qv2 qvr  3H0 2 8G 0.693 t
 Nm V Q 40r Gm r

4 9702/4 M/J/02 Answer all the questions in the spaces provided. 1 (a) The Earth may be considered to be a uniform sphere of radius 6.38 ×106m. Its mass is assumed to be concentrated at its centre. Given that the gravitational field strength at the Earth’s surface is 9.81 N kg–1, show that the mass of the Earth is 5.99 ×1024kg. [2] (b) A satellite is placed in geostationary orbit around the Earth. (i) Calculate the angular speed of the satellite in its orbit. angular speed = … rad s–1 [3] (ii) Using the data in (a), determine the radius of the orbit. radius = … m [3] For Examiner’s Use

5 9702/4 M/J/02 [Turn over 2 Some water in a saucepan is boiling. (a) Explain why (i) external work is done by the boiling water, … … … (ii) there is a change in the internal energy as water changes to steam. … … … [5] (b) By reference to the first law of thermodynamics and your answers in (a), show that thermal energy must be supplied to the water during the boiling process. … … …[2] For Examiner’s Use

6 9702/4 M/J/02 3 (a) (i) The kinetic theory of gases leads to the equation
 m<c2> =  kT. Explain the significance of the quantity
 m<c2>. … … (ii) Use the equation to suggest what is meant by the absolute zero of temperature. … … [3] (b) Two insulated gas cylinders A and B are connected by a tube of negligible volume, as shown in Fig. 3.1. Fig. 3.1 cylinder A cylinder B tap For Examiner’s Use

7 9702/4 M/J/02 [Turn over Each cylinder has an internal volume of 2.0 ×10–2m3. Initially, the tap is closed and cylinder A contains 1.2 mol of an ideal gas at a temperature of 37 °C. Cylinder B contains the same ideal gas at pressure 1.2 ×105Pa and temperature 37 °C. (i) Calculate the amount, in mol, of the gas in cylinder B. amount = … mol (ii) The tap is opened and some gas flows from cylinder A to cylinder B. Using the fact that the total amount of gas is constant, determine the final pressure of the gas in the cylinders. pressure = … Pa [6] For Examiner’s Use

8 9702/4 M/J/02 4 (a) (i) Define simple harmonic motion. … … … (ii) On the axes of Fig. 4.1, sketch the variation with displacement x of the acceleration a of a particle undergoing simple harmonic motion. [4] Fig. 4.1 (b) A strip of metal is clamped to the edge of a bench and a mass is hung from its free end as shown in Fig. 4.2. Fig. 4.2 clamp metal strip mass 0 a x 0 For Examiner’s Use

9 9702/4 M/J/02 [Turn over The end of the strip is pulled downwards and then released. Fig. 4.3 shows the variation with time t of the displacement y of the end of the strip. Fig. 4.4 On Fig. 4.4, show the corresponding variation with time t of the potential energy Ep of the vibrating system. [3] (c) The string supporting the mass breaks when the end of the strip is at its lowest point in an oscillation. Suggest what change, if any, will occur in the period and amplitude of the subsequent motion of the end of the strip. period: … amplitude: …[2] Ep 0.05 0 0.10 0.15 0.20 t / s y 0 0.05 0 0.10 0.15 0.20 t / s 0 For Examiner’s Use Fig. 4.3

10 9702/4 M/J/02 5 (a) Define potential at a point in an electric field. … …[2] (b) An isolated metal sphere of radius r carries a charge +Q. The charge may be assumed to be concentrated at the centre of the sphere. (i) State, in terms of r and Q, the electric potential V at the surface of the sphere. Identify any other symbols you use. … … (ii) Write down the relationship between capacitance C, charge Q and potential V. … (iii) Hence show that the capacitance C of the sphere is given by C = 4πε0r. [3] For Examiner’s Use

11 9702/4 M/J/02 [Turn over (c) The sphere in (b) has a radius of 15 cm and carries a charge of 2.0 ×10–6C. Calculate (i) the capacitance of the sphere, capacitance = … µF (ii) the energy stored on the sphere. energy = … J [4] For Examiner’s Use

12 9702/4 M/J/02 6 (a) Two similar coils A and B of insulated wire are wound on to a soft-iron core, as illustrated in Fig. 6.1. Fig. 6.1 When the current I in coil A is switched on and then off, the variation with time t of the current is shown in Fig. 6.2. Fig. 6.2 Fig. 6.3 On Fig. 6.3, draw a graph to show the variation with time t of the e.m.f. E induced in coil B. [3] E 0 t 0 I t coil A coil B soft-iron core For Examiner’s Use

13 9702/4 M/J/02 [Turn over (b) Fig. 6.4 is the circuit of a bridge rectifier. Fig. 6.4 An alternating supply connected across PR has an output of 6.0 V r.m.s. (i) On Fig. 6.4, circle those diodes that are conducting when R is positive with respect to P. [1] (ii) Calculate the maximum potential difference between points Q and S, assuming that the diodes are ideal. potential difference = … V [2] (iii) State and explain how a capacitor may be used to smooth the output from the rectifier. You may draw on Fig. 6.4 if you wish. … … …[3] P Q load S R For Examiner’s Use

14 9702/4 M/J/02 7 Electrons are emitted from a metal surface when it is illuminated with suitable electromagnetic radiation. (a) Name the effect described above. …[1] (b) The variation with frequency f of the maximum kinetic energy Ek of the emitted electrons is shown in Fig. 7.1. Fig. 7.1 Use Fig. 7.1 to determine (i) the threshold frequency of the radiation, threshold frequency = … Hz (ii) a value for the Planck constant. Planck constant = … J s [4] 0 0 2 4 Ek / 10–19J f / 1014Hz 6 8 4 8 12 16 20 For Examiner’s Use

15 9702/4 M/J/02 (c) On Fig. 7.1, draw a line to show the variation with frequency f of the maximum kinetic energy Ek of the emitted electrons for a second metal which has a lower work function than that in (b). [2] (d) The kinetic energy of the electrons is described as the maximum. Suggest why emitted electrons are likely to have a range of values of kinetic energy for any one frequency of the electromagnetic radiation. … … …[2] For Examiner’s Use

CAMBRIDGE INTERNATIONAL EXAMINATIONS JUNE 2002 GCE Advanced Level MARK SCHEME MAXIMUM: MARK : 60 SYLLABUS/COMPONENT :9702 /4 PHYSICS (STRUCTURED QUESTIONS (A2 CORE)) BES) University of CAMBRIDGE SF Local Examinations Syndicate

age Mark Scheme ylabus | Paper | A Level Examinations — June 2002 [__9702 A Categorisation of marks The marking scheme categorises marks on the MACB scheme. B marks: These are awarded as independent marks, which do not depend on other marks. For a B-mark to be scored, the point to which it refers must be seen specifically in the candidate’s answer. M marks: These are method marks upon which A-marks (accuracy marks) later depend. For an M-mark to be scored, the point to which it refers must be seen in the candidate’s answer. Ifa candidate fails to score a particular M-mark, then none of the dependent A-marks can be scored. C marks: These are compensatory method marks which can be scored even if the points to which they refer are not written down by the candidate, providing subsequent working gives evidence that they must have known it. For example, if an equation carries a C-mark and the candidate does not write down the actual equation but does correct working which shows he/she knew the equation, then the C-mark is awarded. A marks: These are accuracy or answer marks which either depend on an M-mark, or allow a C-mark to be scored, Conventions within the marking scheme BRACKETS Where brackets are shown in the marking scheme, the candidate is not required to give the bracketec information in order to earn the available marks. UNDERLINING In the marking scheme, underlining indicates information that is essential for marks to be awarded.

[ Page 2 l Mark Scheme Syllabus | Paper | [ A Level Examinations — June 2002 9702 4 1 (a) g = GM/R Cl M = 9.81 x (6.38 x 109° / 6.67 x 10°" = 5.99 x10 Kg oe eeeceeeeeeeeceeeeee AO [2] (allow 2 marks if g = 9.8 N kg” used, I mark ifg = 10 N kg" used) (b) () T= Whours eee @ = 2n/(24x« 3600) or2n/T . 727x107 rads" (ii) mra® = GMm/ P = 7.55 x 10” r= 4.23x10'm (3) fee Mee I GB] 2 (a) (i} volume increases on evaporation so work done pushing back the atmosphere (ii) £, of atoms constant (as no temperature change) E, changes because separation of atoms changes so intemal energy changes because U = £, + E, [5] {b) AU = AW + AG argument leading to AQ being positive {2] 3 (a) (i) mean kinetic energy of the atoms / molecules / particles .. (ii) at absolute zero, atoms have no kinetic energy (3] (b) (i) p¥ = nRT n = (1.2 x 10° x 2.0 x 107) 8.31 x 310) = 0.93 mol {ii} total amount = (1.20 + 0.93) (1.20 + 0.93) = (4.0 x 10? x p)/(8.31 x 310) p = 137x10°Pa [6}

Page 3 Mark Scheme Syllabus | Paper A Level Examinations — June 2002 9702 4 4 (a) (i) acceleration proportional to distance (from fixed point) /displacement … Mi and directed towards fixed point oe (ii) graph: straight line through origin MI in quadrants 2 and 4 Al (b) graph: sinusoidal curve, all above t-axis Bi correct period correct ‘phase’ (©) period shorter amplitude larger 5 (a) work done in moving unit (positive) charge from infinity to the point and charge is positive Al (b) () V= Q/4ner where & is permittivity (of free space) Bi (ii) C = Q/V Bl (iii) hence C = 4nqr Bl (€) IC = 4nx 8.85 x 10 x 0.15 = 1.67« 10° pF Bl 2 energy = %CV’ or KOV … C1 potential = (2.0 x 10°)/(1.67 x 10V) = 1.2 109V cece Cl energy = 4x 1.67x 10"! x (1.2 x 10° HS OAZT eee eens cece eee e sce e esac eeeeteeega pea eeeegeeeeee Al 6 (a) sketch: peaks in opposite directions in correct regions Bi no e.m.f. when current constant … . BI correct shape for one of the pulses Bl (b) (i) two correct diodes circled . Bl (ii) Vinax = ¥2 x Vans Cl = 8.48V Al (iii) capacitor connected across SQ Bl discharges through load when p.d. / current in load reduces » Bl thus maintains p.d. across load (or other relevantcomment) … . Bl [4] [3] (2) (2) (3} (4) (3) {1} (2} B]

7 (a) photoelectric effect oo ee eeeeeeeeereeeeneeseceeeceeeeeneneseeserenneeeeeas BI (b) (i) reasonable line extrapolated oo... ceceeeceeeeeeeeceeeeeceaueeeeeeseeeeneeeeeeeeees 6.8 x 10"* Hz (allow + 0.4 x 10!'* Hz) (ii) attempt at finding gradient working shown to give 6.6 x 10 J s Hz (allow + 0.4 x 10" Hz) (c) line: same gradient to the left of the line drawn by candidate (d) — maximum corresponds to electron emitted from surface other electrons require energy to be brought to the surface C Page 4 I Mark Scheme [_Syllabus | Paper [ A Level Examinations — June 2002 [9702 4 {] (4] (Q] (2)