Cambridge A Level Physics 9702 — 2015 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate a metre rule rocking on a beaker. (a) Assemble the apparatus as shown in Fig. 1.1 with the beaker horizontal. The centres of each of the two masses should be at the same distance r from the centre of the metre rule, where r is approximately 30 cm. mass mass r r metre rule label ¶723· beaker modelling clay A bench Fig. 1.1 (b) (i) Measure and record the distance r. r = ...............................................[1] (ii) Adjust the position of the metre rule on the beaker so that the metre rule is balanced and approximately parallel to the bench. (c) (i) Hold down the end of the metre rule on A, as shown in Fig. 1.2. (ii) Release the metre rule and measure and record the time T for it to move up and then down again to its lowest position, as shown in Fig. 1.2. metre rule A Fig. 1.2 T = ............................................ s [2] (d) Reposition the two masses at a different distance r from the centre of the metre rule and repeat (b) and (c) until you have six sets of values of r and T. Use values of r less than or equal to 40 cm. Include values of r 2 and T 3 in your table. [9] (e) (i) Plot a graph of T 3 on the y-axis against r 2 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] (f) The quantities T and r are related by the equation T 3 = a r 2 + b where a and b are constants. Use your answers from (e)(iii) to determine the values of a and b. Give appropriate units. a = ................................................... b = ................................................... [2] You may not need to use all of the materials provided.

Mark scheme: 1 (b) (i) Value of r in the range 28.0 cm to 32.0 cm, with unit. [1] (c) (ii) Value of T in range 2.0 s to 4.0 s. If out of range, allow Supervisor’s value ±20%. [1] Evidence of repeat measurements for T. [1] (d) Six sets of readings of r and T scores 4 marks, five sets scores 3 marks etc. [4] Incorrect trend –1. Help from Supervisor –1. Range: [1] rmax – rmin ≥ 30 cm. Column headings: [1] Each column heading must contain a quantity and a unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. r2 / m2. Consistency: [1] All values of r must be given to the nearest mm. Significant figures: [1] The number of significant figures for every value of T 3 must be the same as, or one more than, the number of significant figures in the corresponding time. Calculation: [1] Values of T 3 calculated correctly to the number of significant figures given by the candidate. (e) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10) are not allowed. Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart. Plotting: [1] All observations in the table must be plotted on the grid. Diameter of plotted points must be ≤ half a small square (no “blobs”). Plotted points must be accurate to within half a small square. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. All points must be within ± 2 s3 of a straight line in the T 3 direction. (ii) Line of best fit: [1] 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 (i.e. circled or labelled) by the candidate. Lines must not be kinked or thicker than half a square. (iii) Gradient: [1] The hypotenuse of the triangle must be greater than half the length of the drawn line. The method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Correct read-offs from a point on the line substituted into y = mx + c or an equivalent expression. Read-offs must be accurate to half a small square in both x and y directions. Or: Intercept read directly from the graph, with read-off accurate to half a small square. (f) Value of a = candidate’s gradient and value of b = candidate’s intercept. [1] Units for a and b are correct (e.g. s3 m–2 for a and s3 for b). [1]

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2 In this experiment, you will investigate how the optical properties of a lens depend on its shape. (a) (i) Select one of the two glass lenses. (ii) Take measurements to determine the thickness t, diameter D and edge height h of the lens, as shown in Fig. 2.1. h t D Fig. 2.1 t = ............................................. cm D = ............................................. cm h = ............................................. cm [3] (b) Calculate R, where D 2 + (t – h)2 R = . 4(t – h) R = ........................................ cm [2] (c) You are provided with a small card which names a bright object in your exam room. You are also provided with a white screen. (i) Use the lens to focus a sharp image of the bright object onto the screen, as shown in Fig. 2.2. sharp image here f bright object screen lens Fig. 2.2 (not to scale) (ii) Measure the distance f from the lens to the screen, as shown in Fig. 2.2. f = ........................................ cm [1] (iii) Estimate the percentage uncertainty in your value of f. percentage uncertainty = .............................................. [1] (d) Using the second lens, repeat (a)(ii), (b), (c)(i) and (c)(ii). t = ............................................. cm D = ............................................. cm h = ............................................. cm R = ............................................. cm f = ............................................. cm [2] Question 2 continues on page 10.

Mark scheme: 2 (a) (ii) Value for t in range 0.10 cm to 0.90 cm and given to nearest 0.01 cm. [1] Value for D in range 3.0 cm to 6.0 cm. [1] Value for h less than t. [1] (b) Correct calculation of R. [1] Value of R given to 2 or 3 significant figures. [1] (c) (ii) Value for f in range 13.0 cm to 17.0 cm or 28.0 to 32.0 cm. [1] (iii) Absolute uncertainty in f in range 0.2 cm to 0.5 cm and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown. [1] (d) Second values for t, D and h. [1] Second value for f. [1] (e) (i) Two values of k calculated correctly. [1] Quality: Both k values in range 0.50 to 1.50. [1] (ii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] (f) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Two readings are not enough to Take more readings and plot a “repeat readings”/ draw a valid conclusion graph / “few readings”/ obtain more k values and only one reading/ compare take more readings and (calculate) average k B Reason for difficulty in measuring t, Use a travelling microscope References to h or D e.g. jaws of calipers slip off parallax ends of lens/jaws too short and cannot reach centre of lens C h is small/large uncertainty in h Use micrometer/travelling microscope D Difficult to obtain sharp image/hard Use a dark(ened) room/ to focus/blurred image turn off lights/ use point/more compact source of light E Difficult to measure f/take Mount lens in holder/clamp/ Flexible/bendy measurement with ruler/measure fix lens to bench with e.g. screens distance, with reason e.g. difficult Blu-Tack/ to keep lens steady/screen not use optical bench vertical/lens not vertical/ruler not perpendicular to lens or screen

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