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

1 In this experiment, you will investigate the oscillations of a pendulum on a board. (a) • Fix the string of the pendulum onto the nail using some of the adhesive putty, as shown in Fig. 1.1. nail board adhesive putty S L ≈ 1.5 cm string bob Fig. 1.1 • The distance between the two edges of the board is S, as shown in Fig. 1.1. The length L of the pendulum is the distance between the centre of the nail and the centre of the bob. Adjust the length of the pendulum by wrapping the string around the nail so that the centre of the bob is approximately 1.5 cm from the edge of the board. • Measure and record S and L. S = .......................................................... cm L = .......................................................... cm [1] (b) • Set up the apparatus as shown in Fig. 1.2. stand clamp nail board string boss bob h adhesive putty bench Fig. 1.2 • The distance between the lower edge of the top of the board and the bench is h, as shown in Fig. 1.2. Adjust the position of the boss so that h is approximately 22 cm. • Fix the position of the bottom of the board using adhesive putty. • Measure and record h. h = .......................................................... cm • Move the bob to the edge of the board, as shown in Fig. 1.3. Fig. 1.3 • Release the bob. The bob rolls across the board and the pendulum oscillates. • Take measurements to determine the period T of the oscillations. T = ............................................................. s [2] (c) Change h in the range 10.0 cm G h G 38.0 cm and determine T. Repeat until you have six sets of values of h and T. S 2 Record your results in a table. Include values of and T in your table. h [8] 2 S(d) (i) Plot a graph of T on the y-axis against on the x-axis. [3] h (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (e) (i) It is suggested that the quantities T, S and h are related by the equation 2 S T = A + B h where A and B are constants. Using your answers in (d)(iii), determine the values of A and B. Give appropriate units. A = ............................................................... B = ............................................................... [2] (ii) Theory suggests that 28π2L A = 5g where g is the acceleration of free fall. Use your values in (a) and (e)(i) to determine a value for g. Give an appropriate unit. g = ......................................................... [1] [Total: 20]

Mark scheme: Question Answer Marks 1(a) Value of S in the range 38.0 cm to 42.0 cm. 1 1(b) Value of T in the range 1.0 s to 4.0 s. 1 Repeats: At least two values of nT, time where n ⩾ 2. 1 1(c) Six (or more) sets of readings of h (different values) and time, nT or T with the correct trend (as h increases , T decreases 3 ) scores 3 marks, five sets scores 2 marks etc. Range: at least one reading of h ⩾ 33.0 cm and 1 at least one reading of h ⩽ 15.0 cm Column headings: Each column heading must contain a quantity and a unit where appropriate. 1 S The presentation of quantity and unit must conform to accepted scientific convention e.g. no unit for and T 2 / s2 or h T 2 (s2) Consistency: 1 All values of raw h must be given to the nearest 0.1 cm. S 1 Significant figures: All values of must be given to the same s.f. as (or one more than) the least s.f. in raw h and S values. h S 1 Calculation: Values of are correct. h 1(d)(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: Trend of points must be positive. 1 All points in the table must be plotted on the grid for this mark to be awarded. S It must be possible to draw a straight line that is within 0.2 (to scale) on the axis (normally x-axis) of all plotted points. h 1(d)(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(d)(iii) Gradient: gradient sign on answer line consistent with graph drawn. 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. 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(e)(i) Value of A = candidate’s gradient value and 1 value of B = candidate’s y-intercept value. The values must not be written as fractions or given to only one significant figure.

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2 In this experiment, you will investigate the resistance of a light-dependent resistor (LDR) using the light from a light-emitting diode (LED). (a) (i) • Using the LED, set up the circuit shown in Fig. 2.1. 3 V d.c. + P LED wire W F Q + V Fig. 2.1 • Ensure that the positive terminal of the power supply and the positive terminal of the LED are connected as shown in Fig. 2.1. • P and Q are crocodile clips. Position P and Q so that there is approximately 10 cm of wire W between P and Q. • Close the switch. The LED should light. • Open the switch. • Using the LDR and ohmmeter, set up a second circuit as shown in Fig. 2.2. ohmmeter Ω LDR Fig. 2.2 • Arrange the apparatus as shown in Fig. 2.3. clamp boss to ohmmeter component holder LDR d stand LED component holder to LED circuit bench Fig. 2.3 (not to scale) • The distance between the top of the LED and the surface of the LDR is d. Adjust the position of the LDR so that d is approximately 0.03 m. • Measure and record d. d = ...................................................... m [2] (ii) Estimate the percentage uncertainty in your value of d. Show your working. percentage uncertainty = ......................................................% [1] (b) • The length of wire W between P and Q is L. Measure and record L. L = ............................................................... • Close the switch. • The potential difference V across the LED is given by the voltmeter. The resistance R of the LDR is given by the ohmmeter. Measure and record V and R. V = ............................................................... R = ............................................................... • Open the switch. [2] (c) • Change the length of wire W between P and Q so that L is approximately 90 cm. • Repeat (b). L = ............................................................... V = ............................................................... R = ............................................................... [3] (d) It is suggested that the relationship between V, d and R is Zd V = + k R where Z has the value 1.00 × 103 V Ω m–1 and k is a constant. (i) Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ............................................................... [1]

Mark scheme: 2(a)(i) Final d value in the range 0.025 m to 0.035 m 1 Raw d measured to the nearest 0.001 m. 1 2(a)(ii) Absolute uncertainty in d in range 0.002 m to 0.006 m 1 Correct method of calculation to find percentage uncertainty e.g. absolute uncertainty/value from (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) Circuit set up without help from the Supervisor, V value with unit in the range 1.0 V to 3.0 V 1 Circuit set up without help from the Supervisor, R value with unit in range 0.20 k to 20 k (200  to 20 000 ) 1 2(c) Second value of L 1 Second values of V and R 1 Second value of R larger than first value of R 1 2(d)(i) 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(d)(ii) Justification for significant figures in k linked to significant figures in V, d, R and Z. 1 2(e) Calculation of percentage difference between candidate’s two k values and comparison of percentage difference with 5%, 1 leading to a consistent conclusion. 2(f) Value of determined. 1 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 wtte e.g. reference to relationship. B Difficulty with aligning the LDR and LED or difficulty positioning the LDR above the LED C Difficult to measure d with a reason e.g. parallax error / cannot identify top of LED / ruler not steady or large % uncertainty in d D Wire short circuits or poor connections with crocodile clips. E Value R is affected by (changes in) ambient light. F Change in R is small with reason e.g. LED not bright enough, difference between ambient light and LED too small. 2(g)(ii) 4 1 mark for each point up to a maximum of 4. A Take more readings (for different values of d) and plot a graph or take more readings and compare k values B Method to improve aligning e.g. use a set square with detail, use a plumbline. C Method to improve measuring d e.g. Use calipers / pointers on rule / travelling microscope / clamp rule (for measuring d). D Mount wire on a strip / use a variable resistor (instead of the wire) / fixed resistors (instead of the wire)/ improved method of connection e.g. soldering E Place LDR and LED in a tube / conduct experiment in a dark room. F Method to produce a larger change in R e.g. use a longer wire W, brighter LED, lower resistor F, higher resistivity of wire W, thinner wire W.

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