Cambridge A Level Physics 9702 — 2024 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate the motion of a loaded metre rule. (a) ● Set up the apparatus as shown in Fig. 1.1. jaws of clamp rod of clamp boss springs string loop attached to springs stand string loop attached to slotted mass slotted mass bench Fig. 1.1 ● Place the slotted mass in the string loop attached to the springs. ● Pull the slotted mass downwards through a small distance. ● Release the mass. The mass will oscillate. ● Determine the period T0 of the oscillations of the mass. T0 = ............................................................... ● Remove the slotted mass from the string loop attached to the springs. [2] (b) ● Set up the apparatus as shown in Fig. 1.2. boss rod of clamp x 50 cm mark boss B nail string loop metre rule slotted mass stand Fig. 1.2 ● Position the string loop attached to the springs at the 50 cm mark on the rule. This string loop must remain in this position throughout the experiment. ● The distance between the string loop supporting the slotted mass and the end B of the rule is x. Position the mass so that x is approximately 20 cm. ● Adjust the apparatus so that the rule is parallel to the bench and the springs are vertical. ● Record x. x = ............................................................... ● Pull B downwards through a small distance. ● Release B. The rule will oscillate. ● Determine the period T of the oscillations of the rule. T = ............................................................... [1] (c) Change x by moving the mass along the rule. For each value of x, adjust the apparatus so that the rule is parallel to the bench and the springs are vertical, then determine T. Repeat until you have six sets of values of x and T with x in the range 10 cm < x < 40 cm. Record your results in a table. Include values of (T – T0)2 in your table. [9] (d) (i) Plot a graph of (T – T0)2 on the y-axis against x 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] (e) It is suggested that the quantities T, T0 and x are related by the equation (T – T0)2 = – Px + Q where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of T0 in the range 0.45 –0.65 s with unit. 1 Evidence of repeats of nT0 where n ⩾ 5. 1 1(b) Value of T  T0. 1 1(c) Six sets of readings of x (different values) and time with correct trend (T decreases as x increases) and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: xmin ⩽ 10.0 cm and xmax = 40.0 cm. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit should conform to scientific convention e.g. (T  T0)2 / s2. 1 Consistency: All raw values of x given to the nearest mm. 1 Calculation: Correct calculation of (T  T0)2. 1 1(d)(i) Axes: 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. Scales must not be awkward (e.g. 3:10 or fractions). 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 in both the x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend must be correct. It must be possible to draw a straight line that is within  2 cm (to scale) on the x- axis of all plotted points. 1 Question Answer Marks 1(d)(ii) Line of best fit: ‘Best fit’ is judged by 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. Line must not be kinked or thicker than half a small 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 5 points left after the anomalous point is disregarded. 1 1(d)(iii) Gradient: 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. The method of calculation must be correct, not x / y. The gradient sign on the answer line must be consistent with the graph drawn. 1 y-intercept: Correct read-off from a point on the line and substituted correctly into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both the x and y directions. or Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square in y direction. 1 1(e) Value of P =  candidate’s gradient and value of Q = candidate’s intercept. The values must not be written as fractions or given to only one significant figure. 1 Units for P: s2 m–1 or s2 cm–1 consistent with x measurement and units for Q: s2. 1

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2 In this experiment, you will investigate the optical properties of glass jars. You have been provided with two glass jars A and B, each containing water. Each jar has a lid. (a) The diameter of jar A is D, as shown in Fig. 2.1. jar A D Fig. 2.1 Measure and record D. D = ......................................................... [1] (b) (i) ● Hold the nail next to jar A, as shown in Fig. 2.2. jar A water nail eye bench Fig. 2.2 ● Close one eye and look at the nail through the water. The bottom of the nail seen through the water will appear to be wider than the top of the nail, as shown in Fig. 2.3. Fig. 2.3 ● Move the nail away from the jar. The bottom of the nail will appear to become wider until it suddenly disappears. Hold the nail at this point. ● The distance between the nail and jar A is y, as shown in Fig. 2.4. y Fig. 2.4 Measure and record y. y = ......................................................... [2] (ii) Estimate the percentage uncertainty in your value of y. Show your working. percentage uncertainty = ..................................................... % [1] (iii) The radius r of jar A is given by D r = . 2 Calculate (r + y). (r + y) = ......................................................... [1] (c) Repeat (a), (b)(i) and (b)(iii) using jar B. D = ............................................................... y = ............................................................... (r + y) = ............................................................... [3]

Mark scheme: 2(a) Value(s) of raw D to the nearest mm with unit. 1 2(b)(i) Raw value(s) of y to the nearest mm with unit. 1 Evidence of repeats of y. 1 2(b)(ii) Percentage uncertainty in y based on absolute uncertainty in the range 2–10 mm. Correct method of calculation to obtain percentage uncertainty e.g. (absolute uncertainty / value from (b)(i))  100. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero) provided the working is shown clearly. 1 2(b)(iii) Correct calculation of (r + y). 1 2(c) Second value of D. 1 Second value of y. 1 Second value of y  first value of y. 1 2(d)(i) Two values of k calculated correctly. The final k values must not be written as fractions or given to only one significant figure. 1 2(d)(ii) Justification for significant figures in k linked to significant figures in D and (r + y). 1 2(e) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 20%, leading to a consistent conclusion. 1 2(f) Value of y and correct calculation of r with unit using candidate’s second value of k. 1 Question Answer Marks 2(g)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure D with a reason e.g. lid in the way / bevelled edges at top or bottom / diameter at top different to rest of jar / parallax error. C Difficult to judge/determine when nail disappears. D Difficult to measure jar y with a reason e.g. parallax error / holding the nail in place / moving nail in correct line. E Difficult to measure lens y because the lens has to be held by hand. F k for glass jar with water may not be suitable to apply for a glass lens (or words to that effect). 1 mark for each point up to a maximum of 4. 4 2(g)(ii) A Take more readings (for different values of D) and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Use calipers (to measure D). C Use a white screen behind nail. D Method to hold nail in position e.g. clamp/adhesive putty/base for nail or put jar and nail on strip with scale markings or guide for nail. E Clamp lens / use lens holder. F Measure k using a solid glass cylinder. 1 mark for each point up to a maximum of 4. 4

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