Cambridge A Level Physics 9702 — 2025 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the equilibrium of a wooden rod. Some of the apparatus has been set up for you. (a) (i) • Fig. 1.1 shows the rod with two eyes. eye eye rod S Fig. 1.1 The distance between the two eyes on the rod is S. Measure and record S. S = ............................................................... • Complete the set-up of the apparatus as shown in Fig. 1.2. stand clamp boss pulley stand string boss clamp mass hanger and masses P Q θ string loop q p bench Fig. 1.2 • P and Q are masses. The distance between the centre of mass P and the centre of the right-hand eye is p, as shown in Fig. 1.2. The distance between the centre of mass Q and the centre of the right-hand eye is q, as shown in Fig. 1.2. The angle between the string and the rod is θ. Use some of the adhesive putty to attach Q to the rod so that q is approximately 26 cm. • Use some of the adhesive putty to attach P to the rod. Adjust the position of P and the position of the stand with the pulley so that the rod is parallel to the bench and θ is approximately 45°. Do not move the stands for the remainder of the experiment. • Measure and record θ, p and q. θ = ............................................................. ° p = ............................................................... q = ............................................................... [2] (ii) The moment of the force about the eye due to mass P is TP . The moment of the force about the eye due to mass Q is TQ. The values of TP and TQ are given by: TP = 5Wp and TQ = 7Wq where W has the value 0.0981 N. Calculate TP and TQ. TP = ............................................................... TQ = ............................................................... [1] (b) Change the position of Q and adjust the position of P until the rod is again parallel to the bench. Measure p and q. Repeat until you have six sets of values of p and q. Record your results in a table. Include values of TP and TQ in your table. [8] (c) (i) Plot a graph of TQ on the y-axis against TP on the x-axis. [3] (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (d) (i) It is suggested that the quantities TQ and TP are related by the equation TQ = A + BTP where A and B are constants. Using your answers in (c)(iii), determine the values of A and B. Give appropriate units. A = ............................................................... B = ............................................................... [2] (ii) Theory suggests that 2A R = F sin θ – S where R is the weight of the rod and F has the value 2.94 N. Use your answers in (a)(i) and (d)(i) to determine a value for R. Give an appropriate unit. R = ......................................................... [1] [Total: 20]

Mark scheme: Question Answer Marks 1(a)(i) RAW θ recorded to the nearest 1° and final value of θ in the range 38° to 52° to the nearest degree 1 Final value of q in range 24.0 cm to 28.0 cm with unit (somewhere) 1 1(a)(ii) Calculation: Values of TP and TQ are correct. 1 1(b) Six (or more) sets of readings of q (different values) and p with the correct trend (as q increases , p decreases ) 4 and without help from supervisor scores 4 marks, five sets scores 3 marks etc. Range: includes qmin ⩽ 22.0 cm and 85.0cm ⩾ qmax ⩾ 32.0 cm and pmax ⩽ 85.0 cm 1 Column headings: 1 Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. TP / N cm Consistency: 1 All RAW values of p and q must be given to the nearest mm. Significant figures: 1 All values of TP and TQ must be given to the same s.f. as (or one more than) the least s.f. in W, p and q values. 1(c)(i) Axes: 1 Axes must be labelled with the correct 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 negative. All points in the table must be plotted on the grid for this mark to be awarded. There must be at least 5 sets of data in the table for this mark to be awarded It must be possible to draw a straight line that is within  2 N cm (0.02 Nm) to scale on the TQ axis (normally y-axis) of all 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 5 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 six or more points are plotted and 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 5 points left after the anomalous point is disregarded. 1(c)(iii) Gradient: 1 Gradient sign on answer line consistent with graph drawn. 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. y-intercept: 1 Either: Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square in y direction. Or Correct read-off from a point on the line is substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. 1(d)(i) Value of A = candidate’s y-intercept value and 1 value of B = candidate’s gradient value. The values must not be written as fractions or given to only one significant figure. Correct unit for A: N m or N cm consistent with the readings 1 Correct unit for B: no unit 1(d)(ii) Correct calculation of R with correct unit (e.g. N) 1

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2 In this experiment, you will investigate the rolling of a plastic bottle. (a) (i) You are provided with a plastic bottle with a cap, as shown in Fig. 2.1. bottle cap d Fig. 2.1 The diameter of the base of the bottle is d. Measure and record d. d = ......................................................... [1] (ii) Estimate the percentage uncertainty in your value of d. Show your working. percentage uncertainty = ..................................................... % [1] (b) • Set up the apparatus as shown in Fig. 2.2. SIDE VIEW stand wooden strip clamp boss metre rules bench ≈ 5 cm Fig. 2.2 • Adjust the two metre rules so that the rules are approximately parallel to each other, as shown in Fig. 2.3. TOP VIEW metre rule wooden strip clamp metre rule Fig. 2.3 • Pour all the water from the beaker into the bottle. • Place the bottle on the two rules as shown in Fig. 2.4. L Fig. 2.4 (not to scale) • Release the bottle. Adjust the rules so that the bottle rolls to the end of the rules. • The distance that the bottle rolls on the rules is L, as shown in Fig. 2.4. Measure and record L. L = ......................................................... [1] (c) (i) • Stand the bottle upright on the bench. • The height of the water in the bottle is h, as shown in Fig. 2.5. water h Fig. 2.5 Measure and record h. h = ............................................................... • The time for the bottle to roll distance L on the rules is t. Take measurements to determine t. t = ............................................................... [3] (ii) A value for the acceleration a of the bottle is given by 2L a = . t 2 Calculate a. a = ......................................................... [1] (iii) Justify the number of significant figures that you have given for your value of a. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a)(i) Final value of d in the range 4.0 cm to 8.0 cm with unit. 1 2(a)(ii) Absolute uncertainty in d in range 0.2 cm to 0.6 cm 1 Correct method of calculation to find percentage uncertainty e.g. absolute uncertainty / value from 2(a)(i))  100. If repeated readings have been taken, then the uncertainty can be half the range if the working is clearly shown, but NOT zero if values are equal. 2(b) Value of L in the range 85.0 cm to 100.0 cm with unit (somewhere) 1 2(c)(i) Raw values of h to the nearest millimetre with unit (seen somewhere) 1 Value of final t in the range 1.0 s to 5.0 s with unit 1 Evidence of repeated measurements of t 1 2(c)(ii) Value of a calculated correctly 1 2(c)(iii) Justification for significant figures in a linked to significant figures in L and t. 1 2(d) Second values of h and t. 1 Second value of t greater than first value of t 1 2(e) 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(f) Calculation of percentage difference between candidate’s two k values and comparison of percentage difference with 15%, 1 leading to a consistent conclusion. 2(g)(i) 1 mark for each point up to a maximum of 4. 4 A Two readings are not enough to draw a conclusion or not enough k values to draw a conclusion B Difficulty with measuring d or diameter with reason e.g. parallax / base / bottom of the bottle is not uniform / edges of the base / bottom of the bottle is curved C Difficult to set / measure the value of L / length with a reason e.g. difficult to place the bottle in the exact same place each time / cannot judge the centre line of the bottle / parallax error D Difficult to measure h or height with a reason e.g. bottle distorts view of water / refraction effects / parallax error / non- uniform shape (of bottle) E Difficulty with the bottle rolling / moving down the rulers (in a straight line) with a reason e.g. rulers bend / ruler(s) move (when bottle is rolling) / rulers are not parallel / bottle is not uniform (shape) / wooden strip is not parallel to the bench / rulers are not at the same height F Difficult to measure t / time with a reason e.g. knowing or judging when bottle reaches the end of rulers 2(g)(ii) 1 mark for each point up to a maximum of 4. 4 A Take more readings (for different values of h) and plot a graph or take more readings and compare k values B Use caliper C Method to hold the bottle at the start / top of rulers e.g. (card) stop D Use a straight-sided / uniform (diameter) bottle E Use a (single) plank / ramp or method of fixing rulers (to wooden strip or bench) e.g. adhesive putty, tape G Improved timing method e.g. video (record / film) and with a timer in view / use frame-by-frame

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