Cambridge A Level Physics 9702 — 2004 Oct/Nov Paper 2 · Variant 1

This document consists of 15 printed pages and 1 blank page. SP (NF/JG) S80558 © UCLES 2004 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level and Advanced Level PHYSICS Paper 2 9702/02 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. DO NOT WRITE IN THE BARCODE. DO NOT WRITE IN THE GREY AREAS BETWEEN THE PAGES. For Examiner’s Use 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. 1 2 3 4 5 6 7 Total Candidate Name Centre Number Candidate Number

2 9702/02/O/N/04 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 © UCLES 2004

3 9702/02/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 = –
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 © UCLES 2004

4 9702/02/O/N/04 Answer all the questions in the spaces provided. 1 A student takes readings to measure the mean diameter of a wire using a micrometer screw gauge. (a) Make suggestions, one in each case, that the student may adopt in order to (i) reduce a systematic error in the readings, … … (ii) allow for a wire of varying diameter along its length, … … (iii) allow for a non-circular cross-section of the wire. … … [3] (b) The mean diameter of the wire is found to be 0.50 ± 0.02 mm. Calculate the percentage uncertainty in (i) the diameter, uncertainty = …………………………………. % (ii) the area of cross-section of the wire. uncertainty = …………………………………. % [2] For Examiner’s Use © UCLES 2004

5 9702/02/O/N/04 [Turn over 2 The spectrum of electromagnetic waves is divided into a number of regions such as radio waves, visible light and gamma radiation. (a) State three distinct features of waves that are common to all regions of the electromagnetic spectrum. 1. … 2. … 3. … [3] (b) A typical wavelength of visible light is 495 nm. Calculate the number of wavelengths of this light in a wave of length 1.00 m. number = …………………………. [2] (c) State a typical wavelength for (i) X-rays, wavelength = …………………………. m (ii) infra-red radiation. wavelength = …………………………. m [2] For Examiner’s Use © UCLES 2004

6 9702/02/O/N/04 3 A girl stands at the top of a cliff and throws a ball vertically upwards with a speed of 12 m s–1, as illustrated in Fig. 3.1. Fig. 3.1 At the time that the girl throws the ball, her hand is a height h above the horizontal ground at the base of the cliff. The variation with time t of the speed v of the ball is shown in Fig. 3.2. Fig. 3.2 20 10 0 –10 –20 –30 –40 0 1.0 2.0 3.0 4.0 5.0 v / m s –1 t / s h path of ball For Examiner’s Use © UCLES 2004

7 9702/02/O/N/04 [Turn over Speeds in the upward direction are shown as being positive. Speeds in the downward direction are negative. (a) State the feature of Fig. 3.2 that shows that the acceleration is constant. … [1] (b) Use Fig. 3.2 to determine the time at which the ball (i) reaches maximum height, time = ………………………………. s (ii) hits the ground at the base of the cliff. time = ………………………………. s [2] (c) Determine the maximum height above the base of the cliff to which the ball rises. height = …………………………… m [3] (d) The ball has mass 250 g. Calculate the magnitude of the change in momentum of the ball between the time that it leaves the girl’s hand to time t = 4.0 s. change = …………………………… N s [3] For Examiner’s Use © UCLES 2004

8 9702/02/O/N/04 (e) (i) State the principle of conservation of momentum. … … … [2] (ii) Comment on your answer to (d) by reference to this principle. … … … … [3] For Examiner’s Use © UCLES 2004

9 9702/02/O/N/04 [Turn over 4 A string is stretched between two fixed points. It is plucked at its centre and the string vibrates, forming a stationary wave as illustrated in Fig. 4.1. Fig. 4.1 The length of the string is 75 cm. (a) State the wavelength of the wave. wavelength = …………………………. m [1] (b) The frequency of vibration of the string is 360 Hz. Calculate the speed of the wave on the string. speed = …………………………… m s–1 [2] (c) By reference to the formation of the stationary wave on the string, explain what is meant by the speed calculated in (b). … … … [3] 75 cm For Examiner’s Use © UCLES 2004

10 9702/02/O/N/04 5 (a) A metal wire has an unstretched length L and area of cross-section A. When the wire supports a load F, the wire extends by an amount ∆L. The wire obeys Hooke’s law. Write down expressions, in terms of L, A, F and ∆L, for (i) the applied stress, … (ii) the tensile strain in the wire, … (iii) the Young modulus of the material of the wire. … [3] (b) A steel wire of uniform cross-sectional area 7.9 × 10–7 m2 is heated to a temperature of 650 K. It is then clamped between two rigid supports, as shown in Fig. 5.1. Fig. 5.1 The wire is straight but not under tension and the length between the supports is 0.62 m. The wire is then allowed to cool to 300 K. When the wire is allowed to contract freely, a 1.00 m length of the wire decreases in length by 0.012 mm for every 1 K decrease in temperature. (i) Show that the change in length of the wire, if it were allowed to contract as it cools from 650 K to 300 K, would be 2.6 mm. [2] 0.62 m rigid support wire For Examiner’s Use © UCLES 2004

11 9702/02/O/N/04 [Turn over (ii) The Young modulus of steel is 2.0 × 1011 Pa. Calculate the tension in the wire at 300 K, assuming that the wire obeys Hooke’s law. tension = …………………………… N [2] (iii) The ultimate tensile stress of steel is 250 MPa. Use this information and your answer in (ii) to suggest whether the wire will, in practice, break as it cools. … … [3] For Examiner’s Use © UCLES 2004

12 9702/02/O/N/04 6 Fig. 6.1 shows the variation with applied potential difference V of the current I in an electrical component C. Fig. 6.1 (a) (i) State, with a reason, whether the resistance of component C increases or decreases with increasing potential difference. … … [2] (ii) Determine the resistance of component C at a potential difference of 4.0 V. resistance = …………………….. Ω[2] 0 1.0 2.0 3.0 4.0 5.0 6.0 0 1.0 2.0 3.0 4.0 I / mA V / V For Examiner’s Use © UCLES 2004

13 9702/02/O/N/04 [Turn over (b) Component C is connected in parallel with a resistor R of resistance 1500 Ωand a battery of e.m.f. E and negligible internal resistance, as shown in Fig. 6.2. Fig. 6.2 (i) On Fig. 6.1, draw a line to show the variation with potential difference V of the current I in resistor R. [2] (ii) Hence, or otherwise, use Fig. 6.1 to determine the current in the battery for an e.m.f. of 2.0 V. current = ……………………… A [2] (c) The resistor R of resistance 1500 Ωand the component C are now connected in series across a supply of e.m.f. 7.0 V and negligible internal resistance. Using information from Fig. 6.1, state and explain which component, R or C, will dissipate thermal energy at a greater rate. … … … … [3] C E R 1500 Ω For Examiner’s Use © UCLES 2004

14 9702/02/O/N/04 7 The α-particle scattering experiment provided evidence for the existence of a nuclear atom. (a) State what could be deduced from the fact that (i) most α-particles were deviated through angles of less than 10°, … … … [2] (ii) a very small proportion of the α-particles was deviated through angles greater than 90°. … … … [2] For Examiner’s Use © UCLES 2004

15 9702/02/O/N/04 (b) Fig. 7.1 shows the path AB of an α-particle as it approaches and passes by a stationary gold nucleus. Fig. 7.1 On Fig. 7.1, draw lines (one in each case) to complete the paths of the α-particles passing by the gold nucleus when the initial direction of approach is (i) along line CD, (ii) along line EF. [3] For Examiner’s Use © UCLES 2004 C A E F D B

16 9702/02/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 Subsidiary and Advanced Level MARK SCHEME for the November 2004 question paper 9702 PHYSICS 9702/02 Paper 2 (Structured), 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 2 60 41 37 25 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 AND AS LEVEL MARK SCHEME MAXIMUM MARK: 60 SYLLABUS/COMPONENT: 9702/02 PHYSICS Paper 2 (Structured)

Page 1 Mark Scheme Syllabus Paper A and AS LEVEL – NOVEMBER 2004 9702 2 © University of Cambridge International Examinations 2005 1 (a) (i) e.g. check for zero error (on micrometer)/zero the micrometer B1 (ii) take readings along the length of the wire/at different points B1 (iii) take readings spirally/around the wire B1 [3] (b) (i) 4% A1 (ii) 8% A1 [2] 2 (a) all same speed in a vacuum (allow medium)/all travel in a vacuum (1) transverse/can be polarised (1) undergo diffraction/interference/superposition (1) can be reflected/refracted (1) show properties of particles (1) oscillating electric and magnetic fields (1) transfer energy/progressive (1) not affected by electric and magnetic fields (1) (allow any three, 1 each) B3 [3] (b) 495 nm = 495 x 10-9 m C1 number = 1/(495 x 10-9) = 2.02 x 106 A1 [2] (allow 2 or more significant figures) (c) (i) allow 10-7 → 10-11 m B1 (ii) allow 10-3 → 10-6 m B1 [2] 3 (a) constant gradient/straight line B1 [1] (b) (i) 1.2 s A1 (ii) 4.4 s A1 [2] (c) either use of area under line or h = average speed x time C1 h = ½ x (4.4 – 1.2) x 32 C1 = 51.2 m A1 [3] (allow 2/3 marks for determination of h = 44 m or h =58.4 m allow 1/3 marks for answer 7.2 m)

Page 2 Mark Scheme Syllabus Paper A and AS LEVEL – NOVEMBER 2004 9702 2 © University of Cambridge International Examinations 2005 (d) ∆p = m∆v OR p = mv C1 = 0.25 x (28 + 12) C1 = 10 N s A1 [3] (answer 4 N s scores 2/3 marks) 3 (e) (i) total/sum momentum before = total/sum momentum after B1 in any closed system B1 [2] (ii) either the system is the ball and Earth B1 momentum of Earth changes by same amount B1 but in the opposite direction B1 or Ball is not an isolated system/there is a force on the ball (B1) Gravitational force acts on the ball (B1) causes change in momentum/law does not apply here (B1) [3] (if explains in terms of air resistance, allow first mark only) 4 (a) wavelength = 1.50 m B1 [1] (b) v = f λ C1 speed = 540 m s-1 A1 [2] (c) (progressive) wave reflected at the (fixed) ends B1 wave is formed by superposition of (two travelling) waves B1 this quantity is the speed of the travelling wave B1 [3] 5 (a) (i) F/A B1 (ii) ∆L/L B1 (iii) FL/A.∆L B1 [3] (b) (i) ∆L = 0.012 x 0.62 x 350 M2 = 2.6 mm A0 [2] (ii) 2.0 x 1011 = (F x 0.62)/(7.9 x 10-7 x 2.6 x 10-3) C1 F = 660 N A1 [2]

Page 3 Mark Scheme Syllabus Paper A and AS LEVEL – NOVEMBER 2004 9702 2 © University of Cambridge International Examinations 2005 (iii) either stress when cold = 660/(7.9 x 10-7) = 840 MPa or tension at uts = 198 N M1 either this is greater than the ultimate tensile stress or tension at uts is less then tension in (ii) A1 the wire will snap A1 [3] (Allow possibility for the two ‘A’ marks to be scored as long as some quantitative answer – even if incorrect – has been given for the ‘M’ mark) 6 (a) (i) resistance is ratio V/I (at a point) B1 either gradient increases or I increases more rapidly than V B1 [2] (If states R = reciprocal of gradient, then 0/2 marks here) (ii) current = 2.00 mA C1 resistance = 2 000 Ω A1 [2] (b) (i) straight line from origin M1 passing through (6.0 V, 4.0 mA) (allow ½ square tolerance) A1 [2] (ii) individual currents are 0.75 mA and 1/33 mA C1 current in battery = 2.1 mA A1 [2] (allow argument in terms of P = I2R or IV) (c) same current in R and in C M1 p.d. across C is larger than that across R M1 so since power = VI, greater in C A1 [3] (allow argument in terms of P = I2R or IV) 7 (a) (i) nucleus is small M1 in comparison to size of atom A1 [2] (ii) nucleus is massive/heavy/dense B1 and charged (allow to be scored in (i) or (ii)) B1 [2] (b) (i) symmetrical path and deviation correct w.r.t. position of nucleus B1 deviation less than in path AB B1 (ii) deviation > 90o and in correct direction B1 [3]