Cambridge A Level Physics 9702 — 2021 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate the equilibrium of a metre rule. (a) ● Use the adhesive putty to attach the 100 g mass to the metre rule as close as possible to the 80 cm mark, as shown in Fig. 1.1. L 50 cm mark metre rule 100 g mass 0 cm end 100 cm end Fig. 1.1 ● The distance between the 50 cm mark and the centre of the mass is L. Measure and record L. L = ......................................................... [1] (b) ● Set up the apparatus as shown in Fig. 1.2. boss rod of clamp long string loop metre rule 100 g mass string loop b 50 cm mark supporting spring x spring stand mass m bench Fig. 1.2 ● Suspend the rule from the long string loop at the 50 cm mark on the rule. ● Add the two 50 g masses to the mass hanger to make a total mass m of 110 g. Suspend mass m from the spring. ● Record m. m = ............................................................ g ● The distance between the string loop supporting the spring and the 50 cm mark on the rule is b. The distance between the top of the top loop of the spring and the bottom of the bottom loop of the spring is x, as shown in Fig. 1.2. Adjust the position of the string loop supporting the spring until the rule is horizontal and in equilibrium. ● Measure and record x and b. x = ............................................................... b = ............................................................... [1] (c) Repeat (b) with different values of m until you have six sets of readings. Record m, x and b. Include your values from (b). 1 Record your results in a table. Include values of in your table. b [9] 1(d) (i) Plot a graph of on the y-axis against x on the x-axis. [3] b (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (e) It is suggested that the quantities b and x are related by the equation 1 = Px + Q b where P and Q are constants. Using your answers in (d)(iii), determine values for P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] (f) A student repeats the experiment placing the 100 g mass closer to the 50 cm mark on the rule. Theory suggests that P and Q are both inversely proportional to L. For this experiment, draw a second line on the graph to show the expected results. Label this line W. [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Final value of L with unit and in the range 28.0–32.0 cm. 1 1(b) Raw value(s) of x and b to nearest mm and with units. 1 1(c) Six (or more) sets of readings of x and b (different values) with correct trend (as m decreases, x decreases and b increases) and without help from Supervisor scores 5 marks, five sets scores 4 marks, etc. 5 Range: (mmax – mmin) ⩾ 70 g. 1 Column headings: 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. 1 / b / cm–1 or 1 / b (1 / cm). 1 Significant figures: All values of 1 / b must be given to the same number of significant figures as, or one greater than, the number of significant figures in raw b. 1 Calculation: Values of 1 / b are correct. 1 1(d)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions Axes must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart. 1 Plotting of points: 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. 1 Quality: All points in the table must be plotted (at least 5) on the grid. Trend of points must be correct. It must be possible to draw a straight line that is within ± 0.2 m–1 (± 0.002 cm–1) on the 1 / b axis (normally y-axis) of all plotted points. 1 Question Answer Marks 1(d)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 5 points). There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated by the candidate. There must be at least five points left after the anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1 1(d)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct, i.e. Δy / Δx. Gradient sign on answer line matches graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph at x = 0, accurate to half a small square. 1 1(e) Value of P equal to candidate’s gradient and value of Q equal to candidate’s intercept. Values must not be written as fractions. 1 Unit for P (e.g. cm–2) and unit for Q (e.g. cm–1) correct. 1 1(f) Line W shown with greater gradient. 1

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2 In this experiment, you will investigate how the rate of cooling of a hot liquid depends on its volume. (a) You have been provided with a cup. The diameter of the base of the cup is d, as shown in Fig. 2.1. d Fig. 2.1 Measure and record d. d = ......................................................... [1] (b) ● Pour boiling water into the cup until it is approximately one-third full. ● When the temperature of the water is 75 °C, start the stop-watch. Record this starting temperature θ0. θ 0 = .......................................................... °C ● After two minutes, measure and record the temperature θ. θ = .......................................................... °C ● Calculate Δθ using Δθ = (θ0 − θ). Δθ = .......................................................... °C [1] (c) (i) The height of the water in the cup is h and the diameter of the surface of the water is D, as shown in Fig. 2.2. D h water Fig. 2.2 Measure and record h and D. h = ............................................................... D = ............................................................... [2] (ii) Estimate the percentage uncertainty in your value of h. Show your working. percentage uncertainty = ......................................................... [1] (iii) Calculate C where D3 − d3 C = . D − d C = ......................................................... [1] (iv) Justify the number of significant figures that you have given for your value of C. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (d) ● Empty the cup. ● Repeat (b), (c)(i) and (c)(iii) with the cup approximately two-thirds full. θ 0 = .......................................................... °C θ = .......................................................... °C Δθ = .......................................................... °C h = ............................................................... D = ............................................................... C = ............................................................... [3]

Mark scheme: 2(a) Value of d to the nearest mm with unit. 1 2(b) Correct calculation of temperature change Δθ. 1 2(c)(i) Value of h with unit. 1 D > d. 1 2(c)(ii) Percentage uncertainty based on absolute uncertainty Δh in the range 2–6 mm. If repeat readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(c)(iii) Correct calculation of C. 1 2(c)(iv) Justification for significant figures in C linked to s.f. in D and d or linked to s.f. in (D – d). 1 2(d) Second values of θ0 and θ. 1 Second values of h and D. 1 Temperature decreases in both experiments and second value of Δθ < first value of Δθ. 1 2(e)(i) Two values of k calculated correctly. The final k values must not be written as fractions. 1 2(e)(ii) Valid comment consistent with the calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure h with reason, e.g. scale of ruler does not start at the end/opaque cup/water too hot/rule in water changes water level. C Difficult to measure D with reason, e.g. parallax. D Large % uncertainty (error) in Δθ or thermometer is not precise enough to measure a small change in temperature. E Difficulty with taking temperature at the end of the two-minute period with reason, e.g. cannot look at stop-watch and thermometer simultaneously. 1 mark for each point up to a maximum of 4. 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). B Use a transparent cup/ruler without a space at end/measure (empty depth – depth to water surface) with detailed description e.g. use rod at right angles to a rule across top of cup to reach water surface or cup bottom. C To measure D or inside of cup, use calipers/dividers/vertical pointers/travelling microscope. D Improved method to measure Δθ e.g. more precise thermometer/thermometer reading to 0.1 °C/thinner capillary in thermometer/more sensitive thermometer or allow experiment to go on for more than two minutes. E Method for simultaneous measurement of temperature and time e.g. sound to mark two-minute period/temperature probe linked to data logger system/video with thermometer and timer in view. 1 mark for each point up to a maximum of 4. 4

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