Cambridge A Level Physics 9702 — 2004 Oct/Nov Paper 4 · Variant 1

This document consists of 14 printed pages and 2 blank pages. SP (SLC/GR) S65276/2 © UCLES 2004 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level PHYSICS 9702/04 Paper 4 October/November 2004 1 hour Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen in the spaces provided on the Question Paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. 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. Centre Number Candidate Number Name For Examiner’s Use 1 2 3 4 5 6 7 Total If you have been given a label, look at the details. If any details are incorrect or missing, please fill in your correct details in the space given at the top of this page. Stick your personal label here, if provided.

2 9702/04/O/N/04 © UCLES 2004 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 9702/04/O/N/04 [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 = – ω2x velocity of particle in s.h.m., v = v0 cos ωt v = ± ω √(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 ωt hydrostatic pressure, p = ρgh pressure of an ideal gas, p =
 <c2> radioactive decay, x = x0 exp(– λt) decay constant, λ = critical density of matter in the Universe, ρ0 = equation of continuity, Av = constant Bernoulli equation (simplified), p1 +
 ρv2 1 = p2 +
 ρv2 2 Stokes’ law, F = Arv Reynolds’ number, Re = drag force in turbulent flow, F = Br2ρv2 ρvr  3H0 2 8G 0.693 t
 Nm V Q 40r Gm r © UCLES 2004

4 9702/04/O/N/04 © UCLES 2004 Answer all the questions in the spaces provided. 1 A particle is following a circular path and is observed to have an angular displacement of 10.3°. (a) Express this angle in radians (rad). Show your working and give your answer to three significant figures. angle = …rad [2] (b) (i) Determine tan10.3° to three significant figures. tan10.3° = … (ii) Hence calculate the percentage error that is made when the angle 10.3°, as measured in radians, is assumed to be equal to tan10.3°. percentage error = … [3] For Examiner’s Use

5 © UCLES 2004 9702/04/O/N/04 [Turn over 2 An α-particle (4 2He) is moving directly towards a stationary gold nucleus (197 79Au). The α-particle and the gold nucleus may be considered to be solid spheres with the charge and mass concentrated at the centre of each sphere. When the two spheres are just touching, the separation of their centres is 9.6 x 10–15m. (a) The α-particle and the gold nucleus may be assumed to be an isolated system. Calculate, for the α-particle just in contact with the gold nucleus, (i) its gravitational potential energy, gravitational potential energy = … J [3] (ii) its electric potential energy. electric potential energy = … J [3] (b) Using your answers in (a), suggest why, when making calculations based on an α-particle scattering experiment, gravitational effects are not considered. … …[1] (c) In the α-particle scattering experiment conducted in 1913, the maximum kinetic energy of the available α-particles was about 6 MeV. Suggest why, in this experiment, the radius of the target nucleus could not be determined. … … …[2] For Examiner’s Use

6 9702/04/O/N/04 © UCLES 2004 3 The vibrations of a mass of 150 g are simple harmonic. Fig. 3.1 shows the variation with displacement x of the kinetic energy Ek of the mass. Fig. 3.1 (a) On Fig. 3.1, draw lines to represent the variation with displacement x of (i) the potential energy of the vibrating mass (label this line P), (ii) the total energy of the vibrations (label this line T). [2] (b) Calculate the angular frequency of the vibrations of the mass. angular frequency = … rad s–1 [3] 0 -2 -4 -6 2 4 6 0 4 8 12 16 Ek / mJ x / cm For Examiner’s Use

7 © UCLES 2004 9702/04/O/N/04 [Turn over (c) The oscillations are now subject to damping. (i) Explain what is meant by damping. … … …[2] (ii) The mass loses 20% of its vibrational energy. Use Fig. 3.1 to determine the new amplitude of oscillation. Explain your working. amplitude = … cm [2] For Examiner’s Use

8 9702/04/O/N/04 © UCLES 2004 4 A small coil is positioned so that its axis lies along the axis of a large bar magnet, as shown in Fig. 4.1. Fig. 4.1 The coil has a cross-sectional area of 0.40 cm2 and contains 150 turns of wire. The average magnetic flux density B through the coil varies with the distance x between the face of the magnet and the plane of the coil as shown in Fig. 4.2. Fig. 4.2 (a) (i) The coil is 5.0 cm from the face of the magnet. Use Fig. 4.2 to determine the magnetic flux density in the coil. magnetic flux density = … T 5 0 10 15 20 25 0 20 40 60 80 B / mT x / cm For Examiner’s Use x coil pole of magnet leads to coil axis of coil and magnet

9 © UCLES 2004 9702/04/O/N/04 [Turn over (ii) Hence show that the magnetic flux linkage of the coil is 3.0 x 10–4Wb. [3] (b) State Faraday’s law of electromagnetic induction. … … …[2] (c) The coil is moved along the axis of the magnet so that the distance x changes from x = 5.0 cm to x = 15.0 cm in a time of 0.30 s. Calculate (i) the change in flux linkage of the coil, change = … Wb [2] (ii) the average e.m.f. induced in the coil. e.m.f. = … V [2] (d) State and explain the variation, if any, of the speed of the coil so that the induced e.m.f. remains constant during the movement in (c). … … … …[3] For Examiner’s Use

10 9702/04/O/N/04 © UCLES 2004 5 A charged particle passes through a region of uniform magnetic field of flux density 0.74 T, as shown in Fig. 5.1. Fig. 5.1 The radius r of the path of the particle in the magnetic field is 23 cm. (a) The particle is positively charged. State the direction of the magnetic field. …[1] (b) (i) Show that the specific charge of the particle (the ratio of its charge to its mass) is given by the expression = , where v is the speed of the particle and B is the flux density of the field. [2] v rB q m q m For Examiner’s Use region of uniform magnetic field path of charged particle

11 © UCLES 2004 9702/04/O/N/04 [Turn over (ii) The speed v of the particle is 8.2 x 106m s–1. Calculate the specific charge of the particle. specific charge = … C kg–1 [2] (c) (i) The particle in (b) has charge 1.6 x 10–19C. Using your answer to (b)(ii), determine the mass of the particle in terms of the unified atomic mass constant u. mass = … u [2] (ii) The particle is the nucleus of an atom. Suggest the composition of this nucleus. … …[1] For Examiner’s Use

12 9702/04/O/N/04 © UCLES 2004 6 The isotopes Radium-224 (224 88Ra) and Radium-226 (226 88Ra) both undergo spontaneous α-particle decay. The energy of the α-particles emitted from Radium-224 is 5.68 MeV and from Radium-226, 4.78 MeV. (a) (i) State what is meant by the decay constant of a radioactive nucleus. … … …[2] (ii) Suggest, with a reason, which of the two isotopes has the larger decay constant. … … … …[3] (b) Radium-224 has a half-life of 3.6 days. (i) Calculate the decay constant of Radium-224, stating the unit in which it is measured. decay constant = …[2] (ii) Determine the activity of a sample of Radium-224 of mass 2.24 mg . activity = … Bq [4] For Examiner’s Use

13 © UCLES 2004 9702/04/O/N/04 [Turn over (c) Calculate the number of half-lives that must elapse before the activity of a sample of a radioactive isotope is reduced to one tenth of its initial value. number of half-lives = …[2] For Examiner’s Use

14 9702/04/O/N/04 © UCLES 2004 7 The e.m.f. generated in a thermocouple thermometer may be used for the measurement of temperature. Fig. 7.1 shows the variation with temperature T of the e.m.f. E. Fig. 7.1 (a) By reference to Fig. 7.1, state two disadvantages of using this thermocouple when the e.m.f. is about 1.0 mV. 1. … 2. …[2] (b) An alternative to the thermocouple thermometer is the resistance thermometer. State two advantages that a thermocouple thermometer has over a resistance thermometer. 1. … … 2. … …[2] 300 400 500 600 700 0.5 1.0 1.5 0 E / mV T / K For Examiner’s Use

16 9702/04/O/N/04 BLANK PAGE Every reasonable effort has been made to trace all copyright holders where the publishers (i.e. UCLES) are aware that third-party material has been reproduced. The publishers would be pleased to hear from anyone whose rights they have unwittingly infringed. University of Cambridge International Examinations is part of the University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the November 2004 question paper 9702 PHYSICS 9702/04 Paper 4 (Core), maximum raw mark 60 This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. This shows the basis on which Examiners were initially instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began. Any substantial changes to the mark scheme that arose from these discussions will be recorded in the published Report on the Examination. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes must be read in conjunction with the question papers and the Report on the Examination. • CIE will not enter into discussion or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the November 2004 question papers for most IGCSE and GCE Advanced Level syllabuses.

Grade thresholds taken for Syllabus 9702 (Physics) in the November 2004 examination. minimum mark required for grade: maximum mark available A B E Component 4 60 39 34 18 The thresholds (minimum marks) for Grades C and D are normally set by dividing the mark range between the B and the E thresholds into three. For example, if the difference between the B and the E threshold is 24 marks, the C threshold is set 8 marks below the B threshold and the D threshold is set another 8 marks down. If dividing the interval by three results in a fraction of a mark, then the threshold is normally rounded down.

November 2004 GCE A LEVEL MARK SCHEME MAXIMUM MARK: 60 SYLLABUS/COMPONENT: 9702/04 PHYSICS Paper 4 (Core)

Page 1 Mark Scheme Syllabus Paper A LEVEL – NOVEMBER 2004 9702 4 © University of Cambridge International Examinations 2005 1 (a) θ (rad) = 2π x (10.3/360) 1 = 0.180 rad (n.b. 3 sig. fig.) 1 [2] (b) (i) tan θ = 0.182 (n.b. 3 sig. fig.) 1 (ii) percentage error = (0.002/0.180) x 100 1 = 1.1 (%) 1 [3] (allow 0.002/0.182 and allow 1
4 sig. fig.) 2 (a) (i) grav. pot. energy = GM1M2/R 1 energy = {6.67 x 10-11 x 197 x 4 x (1.66 x 10-27)2}/9.6 x 10-15 1 = 1.51 x 10-47 J 1 [3] (ii) elec. pot. energy = Q1Q2/4πε 0R 1 energy = {79 x 2 x (1.6 x 10-19)2}/4π x 8.85 x 10-12 x 9.6 x 10-15 1 = 3.79 x 10-12 J 1 [3] (For the substitution, -1 each error or omission to max 2 in (i) and in (ii)) (b) electric potential energy >> gravitational potential energy 1 [1] (c) either 6 MeV = 9.6 x 10-13 J or 3.79 x 10-12 J = 24 MeV 1 not enough energy to get close to the nucleus 1 [2] 3 (a) (i) reasonable shape as ‘inverse’ of k.e. line 1 (ii) straight line, parallel to x-axis at 15 mJ 1 [2] (b) either (max) kinetic energy (= ½ mv2) = ½ mω 2a0 2 1 15 x 10-3 = ½ x 0.15 x ω 2 x (5.0 x 10-2)2 1 ω = 8.9(4) rad s-1 1 or (k.e. = ½ mv2), v = 0.44(7) m s-1 1 ω = v/a = (0.447)/(5.0 x 10-2) 1 ω = 8.9(4) rad s-1 1 [3] (c) (i) either loss of energy (from the system) or amplitude decreases or additional force acting (on the mass) 1 either continuous/gradual loss or force always opposing motion 1 [2] (ii) either (now has 80% of its) p.e./k.e. = 12 mJ or loss in k.e. = 3 mJ 1 new amplitude = 4.5 cm (allow ± 0.1 cm) 1 [2]

Page 2 Mark Scheme Syllabus Paper A LEVEL – NOVEMBER 2004 9702 4 © University of Cambridge International Examinations 2005 4 (a) (i) 50 mT 1 (ii) flux linkage = BAN 1 = 50 x 10-3 x 0.4 x 10-4 x 150 = 3.0 x 10-4 Wb 1 [3] (allow 49 mT
2.94 x 10-4 Wb or 51 mT
3.06 x 10-4 Wb) (b) e.m.f./induced voltage (do not allow current) proportional/equal to 1 rate of change/cutting of flux (linkage) 1 [2] (c) (i) new flux linkage = 8.0 x 10-3 x 0.4 x 10-4 x 150 = 4.8 x 10-5 Wb 1 change = 2.52 x 10-4 Wb 1 [2] (ii) e.m.f. = (2.52 x 10-4)/0.30 1 = 8.4 x 10-4 V 1 [2] (d) either for a small change in distance x 1 (change in) flux linkage decreases as distance increases 1 so speed must increase to keep rate of change constant 1 [3] or (change in) flux linkage decreases as distance increases (1) at constant speed, e.m.f/flux linkage decreases as x increases (1) so increase speed to keep rate constant (1) 5 (a) into (plane of) paper/downwards 1 [1] (b) (i) the centripetal force = mv2/r 1 mv2lr = Bqv hence q/m = v/r B (some algebra essential) 1 [2] (ii) q/m = (8.2 x 106)/(23 x 10-2 x 0.74) 1 = 4.82 x 107 C kg-1 1 [2] (c) (i) mass = (1.6 x 10-19)/(4.82 x 107 x 1.66 x 10-27) 1 = 2u 1 [2] (ii) proton + neutron 1 [1] 6 (a) (i) either probability of decay or dN/dt = (-)λN OR A = (-)λN 1 per unit time with symbols explained 1 [2] (ii) greater energy of α particle means 0 (parent) nucleus less stable 1 nucleus more likely to decay 1 hence Radium-224 1 [3] (b) (i) either λ = In2/3.6 or λ = In2/3.6 x 24 x 3 600 = 0.193 = 2.23 x 10-6 1 unit day -1 s-1 1 [2] (one sig.fig., -1, allow λ in hr-1)

Page 3 Mark Scheme Syllabus Paper A LEVEL – NOVEMBER 2004 9702 4 © University of Cambridge International Examinations 2005 (ii) N = {(2.24 x 10-3)/224} x 6.02 x 1023 1 = 6.02 x 1018 1 activity = λN = 2.23 x 10-6 x 6.02 x 1018 1 = 1.3 x 1013 Bq 1 [4] (c) A = A0 e-ln2.tlT 0.1 = exp(-In2 . n) 1 n = 3.32 1 [2] (n = 3 without working scores 1 mark) 7 (a) variation is non-linear 1 two possible temperatures 1 [2] (b) e.g. 1. small thermal capacity/measure ∆θ of small object /short response time 2 readings taken at a point/physically small 3 can be used to measure temperature difference 4 no power supply required etc. (any two, 1 mark each) 2 [2]