Cambridge A Level Physics 9702 — 2024 Oct/Nov Paper 3 · Variant 3

1 In this experiment, you will determine the resistivity of a metal. (a) ● Set up the circuit shown in Fig. 1.1. 1.5 V R V metre rule tape F tape L wire Fig. 1.1 (not to scale) ● The distance between the two crocodile clips is L. The reading on the voltmeter is V. Adjust the position of crocodile clip F so that L is approximately 45 cm. ● Close the switch. ● Record the value of L and the voltmeter reading V. L = .......................................................... cm V = ............................................................ V ● Open the switch. [1] (b) Vary L in the range 15.0 cm G L G 95.0 cm by adjusting the position of F. For each position of F, measure L and V. Repeat until you have six sets of values of L and V. 1 1 Record your results in a table. Include values of and in your table. L V [8] 1 1 (c) (i) Plot a graph of on the y-axis against on the x-axis. [3] V L (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (d) It is suggested that the quantities V and L are related by the equation 1 J = + W V L where J and W are constants. Using your answers in (c)(iii), determine the values of J and W. Give appropriate units. J = ............................................................... W = ............................................................... [2] (e) (i) Use a micrometer to measure the diameter d of the wire. d = ......................................................... [2] (ii) Theory suggests that πd 2WR J = 4ρ where R is 33 Ω and ρ is the resistivity of the metal of the wire. Using your answers in (d) and (e)(i), determine a value for ρ. ρ = .................................................. Ω m [1] [Total: 20]

Mark scheme: Question Answer Marks 1(a) Final value of L in the range 44.0–46.0 cm 1 and final value of V in range 0–2.0 V. 1(b) Six sets of readings of L (different values) and V with the correct trend (as L increases, V increases) and without help from 3 supervisor scores 3 marks, five sets scores 2 marks, etc. Range: Uses L ⩽ 25.0 cm and L ⩾ 85.0 cm. 1 Column headings: 1 Each column heading must contain a quantity and a unit. 1 The presentation of quantity and unit must conform to accepted scientific convention, e.g. / cm–1 L Consistency: All raw values of L must be given to 0.1 cm. 1 1 1 Significant figures: All values of must be given to the same number of s.f. as (or one more than) the number of s.f. in raw V V values. 1 1 Calculation: Values of are correct. V 1(c)(i) Axes: 1 Axes must be labelled with the required quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Scale markings are no more than 2 cm (one large square) apart. Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Plotting of points: 1 All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions. Quality: 1 Trend of points must be positive. All points in the table must be plotted (at least 5) on the grid for this mark to be awarded. 1 It must be possible to draw a straight line that is within  0.5 V–1 ( 0.0005 mV–1) on the axis (normally y-axis) of all V plotted points. 1(c)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least five points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Lines must not be kinked or thicker than half a square. Some candidates may choose to identify an anomalous point. If they identify one point as anomalous (e.g. by circling or labelling) then this point is to be disregarded when judging the line of best fit. There must be at least five points left after the anomalous point is disregarded. 1(c)(iii) Gradient: 1 The hypotenuse of the triangle used should be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both the x and y directions. Method of calculation must be correct (not x / y). Gradient sign on answer line consistent with graph drawn. y-intercept: 1 1 Intercept read directly from the graph, with read-off at = 0, accurate to half a small square in y direction. L or Correct read-off from a point on the line substituted correctly into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. 1(d) J = candidate’s gradient value and W = candidate’s y-intercept value. 1 The values must not be written as fractions, roots or given only to one significant figure. Correct unit for J: V–1 m or V–1 cm 1 and correct unit for W: V–1. 1(e)(i) Value of d in the range 0.200–0.300 mm with unit 1 and all raw values given to either 0.01 mm or all to 0.001 mm. Repeat values of d. 1 1(e)(ii) correctly calculated from J and W: 1 d 2 RW = 4 J Final answer with correct power of ten for .

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2 In this experiment, you will investigate the movement of a ball. (a) You are provided with two table tennis balls A and B, each attached to a string. The mass of A and its string is m. Use the balance to measure m. m = ....................................................... g [1] (b) (i) ● Attach the clamp to the stand using the boss. ● Place both strings between the two wooden strips and secure the wooden strips in the clamp, as shown in Fig. 2.1. clamp wooden strips string stand ≈ 50 cm ball ball block B A bench ≈ 1.5 cm Fig. 2.1 (not to scale) ● Adjust the apparatus so that the bottoms of the two wooden strips are approximately 50 cm above the bench and the bottoms of the two balls are approximately 1.5 cm above the bench. ● Displace A and adjust the position of the block so that, when they are touching, the centre of A is level with the top of the block, as shown in Fig 2.2. block A B d b Fig. 2.2 (not to scale) ● When A is in this position, the distance between the centre of B and the bench is b, as shown in Fig. 2.2. The distance between the top of the block and the bench is d. Measure and record b and d. b = .......................................................... cm d = .......................................................... cm ● Calculate d - b . Give an appropriate unit. d - b = ............................................................... [2] (ii) Justify the number of significant figures that you have given for your value of d - b . ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (iii) ● Release A so that it moves towards B. ● When A hits B, it causes B to move. At the maximum height of ball B, the vertical distance between the centre of B and the bench is H, as shown in Fig. 2.3. B A H Fig. 2.3 (not to scale) Determine H. H = .................................................... cm [2] (iv) Estimate the percentage uncertainty in your value of H. Show your working. percentage uncertainty = ..................................................... % [1] (v) With this arrangement of the apparatus, the total mass of A is equal to m measured in (a). ● Record the total mass M of A. M = ............................................................ g ● Calculate H - b . H - b = ...............................................................

Mark scheme: 2(a) Mass m of A (and string) measured and to the nearest 0.1 g or better. 1 2(b)(i) Value of b in the range 2.0–4.0 cm, recorded to the nearest millimetre 1 and value of d in the range 9.0–11.0 cm, recorded to the nearest millimetre. Value of (d − b ) calculated with correct unit i.e. cm1/2. 1 2(b)(ii) Number of significant figures in (d − b ) must link to number of significant figures in (d – b). 1 2(b)(iii) Final value of H: b < H < d. 1 Evidence of repeats. 1 2(b)(iv) Percentage uncertainty based on absolute uncertainty in H in range 0.3–1.0 cm. 1 Correct method of calculation to find percentage uncertainty e.g. (absolute uncertainty / value from 2(b)(iii))  100. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. 2(b)(v) √(H − b) calculated correctly. 1 2(c) Second values of H and M. 1 Second value of H > first value of H. 1 2(d) Two values of k calculated correctly. 1 The final k values must not be written as fractions or given to only one significant figure. 2(e) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 15% leading to a consistent conclusion. 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficult to measure b with a reason e.g. difficult to locate the centre of the ball / holding ball A whilst measuring at the same time. C Difficult to measure H with reason e.g. difficult to judge when at maximum height / at maximum height for a short period of time / final horizontal position not known. D Difficulty with collision / impact e.g. ball B and ball A are not at the same height / ball A does not hit ball B head- on / glances off at an angle. E Difficulty with mass(es) with reason e.g. mass of adhesive putty not taken into account / mass added is not uniformly distributed / mass not added at the centre of gravity. 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings (for different values of M) and plot a graph or take more readings and compare k values (not 4 “repeat readings” on its own). B Use a clamped rule (to measure b) or measure to the bottom and top of ball or measure diameter of ball and measure to top or bottom of ball or clamp or place stop for ball A (related to measuring b). C Video / record / film with rule in view or place grid behind or trial and error with pointer / stop. D Set up the two strings with two separate clamps (so balls are at the same height at the point of impact). E Specified method to determine / account for the mass of the adhesive putty e.g. measure mass of adhesive putty and add to mass or measure total mass or repeat with heavier ball (A) instead of using extra 10 g mass. 1 mark for each point up to a maximum of 4.

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