Cambridge A Level Physics 9702 — 2025 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the properties of a pendulum. (a) (i) • Assemble the apparatus as shown in Fig. 1.1. upper rod (with hole) hole boss SIDE VIEW 53 cm lower rod boss stand 20 cm bench Fig. 1.1 • Rotate the upper rod in the boss so that the hole is vertical. • Thread the string of the pendulum up through the hole in the upper rod and pull it through until the pendulum bob is approximately 2 cm above the bench. Use the clip to fasten the string to the stand to prevent the string from slipping down through the hole, as shown in Fig. 1.2. string clip FRONT VIEW L1 L2 bob ≈ 2 cm Fig. 1.2 • Turn the lower rod horizontally so that the string is just touching the rod. Leave both rods in these positions for the whole experiment. • The distance of the centre of the bob below the upper rod is L1. The distance of the centre of the bob below the lower rod is L2. Measure and record L1 and L2. L1 = ................................................................ L2 = ................................................................ [1] (ii) • Push the bob so that the string moves a short distance away from the lower rod and then release it. The bob will oscillate. • Take measurements to find the period T of the oscillations. T = .......................................................... [2] (b) Move the string through the hole and refasten it to change L1. Measure and record L1, L2 and T. Repeat until you have six sets of values of L1, L2 and T. Record your results in a table. Include values of ( L1 + L2) to three significant figures in your table. [8] (c) (i) Plot a graph of T on the y‑axis against ( L1 + L2) 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) It is suggested that the quantities T, L1 and L2 are related by the equation T = a( L1 + L2) + b 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] (e) Theory suggests that a is related to the acceleration of free fall g by g = _π 2. ai Using your value for a, calculate a value for g. Give an appropriate unit. g = ......................................................... [1] [Total: 20]

Mark scheme: Question Answer Marks 1(a)(i) Values of L1 and L2 with consistent unit 1 and L2 in the range 15.0–18.0 cm. 1(a)(ii) Value of T on answer line in the range 0.70–1.50 s with unit. 1 Repeats: At least two measurements of nT where n ⩾ 5. 1 1(b) Six sets of readings of L1 (different values), L2 and T with correct trend (as L1 decreases, L2 and average T decreases) and 3 without help from Supervisor scores 3 marks, five sets scores 2 marks etc. Range: At least one value of L2 ⩽ 6.0 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. (L1 + L2) / cm½. Consistency: All values of L1 and L2 must be given to the nearest mm. 1 Significant figures: All values of (L1 + L2) given to 3 significant figures. 1 Calculation: (L1 + L2) calculated correctly. 1 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 points) for this mark to be awarded. It must be possible to draw a straight line that is within ± 0.5 cm½ on the (L1 + L2)-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 6 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. 1(c)(iii) Gradient: 1 The hypotenuse of the triangle used must 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 must be consistent with graph drawn. y-intercept: 1 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) a = candidate’s gradient value and b = candidate’s intercept value. 1 Values must not be written as fractions or given to only one significant figure. Units for a and b correct (e.g. s cm–½ for a and s for b). 1 1(e) Correct calculation for g with consistent unit. 1

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2 In this experiment, you will investigate the motion of steel balls falling through water in a tube. (a) (i) You have been provided with a wide tube attached to a wooden strip. Measure and record the internal diameter D of the wide tube. D = ......................................................... [2] (ii) • Assemble the apparatus as shown in Fig. 2.1. stand wide tube boss tape marker clamp wooden strip tape marker boss tray clamp narrow tube bench Fig. 2.1 You have been provided with four steel balls of two different diameters. • Measure and record the diameter d of one of the larger balls. d = ............................................................... • Fill the syringe with water from the beaker. • Push the nozzle of the syringe securely into the narrow tube. Slowly push the syringe plunger until the wide tube is filled to the top with water. Leave the syringe attached to the narrow tube. • Drop one of the larger balls into the wide tube and watch it fall down past the two tape markers. • Use the magnet to retrieve the ball from the tube. [1] (b) (i) • Drop one of the larger balls into the wide tube. • Take measurements to determine the time t for the ball to fall from the upper tape marker to the lower tape marker. t = ......................................................... [2] (ii) Estimate the percentage uncertainty in your value of t. Show your working. percentage uncertainty = ......................................................% [1] (c) • Measure and record the diameter d of one of the smaller balls. d = ............................................................... • Using one of the smaller balls, repeat (b)(i). t = ............................................................... [3] (d) It is suggested that the relationship between t, D and d is 1 = k(D2 – d2) t where k is a constant. (i) Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ............................................................... [1] (ii) Justify the number of significant figures that you have given for your values of k. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a)(i) Value for D in range 5.00–7.00 mm, with unit 1 Evidence of repeated measurements of D. 1 2(a)(ii) Value for d in range 4.50–5.50 mm with unit and to at least the nearest 0.1 mm. 1 2(b)(i) Value of time in the range 0.8–20.0 s with unit and to the nearest 0.1 s or better. 1 Evidence of repeated measurements of t. 1 2(b)(ii) Percentage based on absolute uncertainty in t of 0.2–0.5 s. 1 Correct method of calculation to obtain percentage uncertainty e.g. (absolute uncertainty / value from (b)(i))  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(c) Second value of d. 1 Second value of t. 1 Value for second t < first t. 1 2(d)(i) Two values of k calculated correctly. 1 The final k values must not be written as fractions. 2(d)(ii) Justification based on the significant figures in t and (D2 – d2). 1 2(e) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 10%, leading to a consistent conclusion. 2(f)(i) A Two (sets of) readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few 4 readings”). B Large percentage uncertainty in t / time. C Difficult to measure t / fall time / time between markers since it is difficult to judge when ball reaches the tape / marker. D Difficult to measure D with reason e.g. tube cross section not circular / tube changes shape when measuring / internal jaws of calipers too big. E Difficult to measure d with reason e.g. difficult to hold ball in jaws of calipers. F Difficulty with balls e.g. difficult to remove balls with magnet / balls hit side of tube when falling. 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). 4 B Increase the fall distance / use a long(er) tube. C Record / film / video with timer in view. D Use glass / rigid tube / use travelling microscope. E Use micrometer screw gauge. F Use strong(er) magnet / have more balls (of each size). 1 mark for each point up to a maximum of 4.

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