Cambridge A Level Physics 9702 — 2023 Feb/March Paper 3 · Variant 3

1 In this experiment, you will investigate the equilibrium of a wooden rod. (a) (i) • Assemble the apparatus as shown in Fig. 1.1 with the nail held securely in the cork. Check that the rod can swing freely. nail cork clamp boss notches L H wooden rod stand bench mass Fig. 1.1 • The height of the nail above the bench is H. Measure and record H. H = ............................................................... This height must be kept constant throughout the experiment. • The distance between the nail and the centre of the mass is L. Measure and record L. L = ............................................................... [1] (ii) • Assemble the remaining apparatus as shown in Fig. 1.2. Place the string loop in a notch near the mid‑point of the rod. stand pulley string loop string θ plumb h line mass Fig. 1.2 • Adjust the height of the pulley so that the string pulling the rod is parallel to the bench. • The height of the string above the bench is h, as shown in Fig. 1.2. Measure and record h. h = ............................................................... • The angle between the plumb line and the rod is θ, as shown in Fig. 1.2. Measure and record θ. θ = ............................................................. ° [1] (b) Move the string loop to another notch and adjust the height of the pulley and the position of its stand so that the string pulling the rod is parallel to the bench. Repeat until you have six sets of values of h and θ. Record your results in a table. Include values of sinθ to 3 significant figures in your table. [9] (c) (i) Plot a graph of sinθ on the y‑axis against h 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 θ and h are related by the equation sinθ = a h + 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) The mass of the wooden rod is M. Calculate M using the relationship 1 ML – = L + a N where N is 200 g. M = ....................................................... g [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a)(i) Value of L in range 43.0 to 47.0 cm, with unit. 1 1(a)(ii) Value of h less than H 1 and  to nearest degree and in range 5° to 40°. 1(b) Six sets of readings of h and with correct trend and without help scores 4 marks, five sets scores 3 marks etc. 4 1(b) Range: 1 min ⩽ 10° and max ⩾ 30° 1(b) 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.  /  sin must not have a unit. 1(b) Consistency: 1 All raw values of h must be given to the nearest mm 1(b) Significant figures: 1 Values of singiven to 3 s.f. 1(b) Calculation: 1 Values of sincalculated correctly 1(c)(i) Axes: 1 Sensible scales are used, no awkward scales (e.g. 3:10) Scales are chosen so that the plotted points occupy at least half the graph grid in both x and y directions Scales are labelled with the quantity which is being plotted. Scale markings are no more than 2 cm apart. 1(c)(i) Plotting of points: 1 All observations from the table are plotted on the grid. Diameters of plotted points are  half a small square (no blobs). Plots are accurate to within half a small square in both x and y directions. 1(c)(i) Quality: 1 All points in the table must be plotted (at least 5) for this mark to be awarded. It must be possible to draw a straight line that is within  0.02 on the sin axis of all plotted points. The trend must be negative. 1(c)(ii) Line of best fit: 1 Judged by balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the line along the full length If all points lie on trend candidates do not need to indicate an anomalous point. However, a single off-trend point is allowed as anomalous if it is circled or labelled and there are at least five other plotted points. Lines must not be kinked or thicker than half a square. 1(c)(iii) Gradient: 1 The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct. Not x / y. Both read-offs must be accurate to half a small square in both the x and y directions. 1(c)(iii) y-intercept: 1 Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at h = zero accurate to half a small square in y direction. 1(d) a equal to candidate’s gradient and b equal to candidate’s intercept. 1 Values must not be written as fractions or to only 1 significant figure. 1(d) Units for a and b correct and consistent with value (e.g. cm–1 for a and no unit for b) 1 1(e) Correct calculation of M 1

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2 In this experiment, you will investigate the properties of sugar solution. (a) • Assemble the apparatus as shown in Fig. 2.1. screen u0 v torch lens transparent container bench modelling clay Fig. 2.1 • The distance from the screen to the centre of the lens is v, as shown in Fig. 2.1. Adjust the apparatus so that v is approximately 40 cm. Measure and record v. v = .......................................................... cm • Switch on the torch and shine the light through the lens. An image of the LEDs in the torch will appear on the screen. • Adjust the distance of the torch from the lens until the image of the LEDs is as sharp as possible. The distance from the front of the torch to the centre of the lens when the image is as sharp as possible is u0, as shown in Fig. 2.1. Measure and record u0. u0 = .......................................................... cm [2] (b) (i) • You have been provided with a beaker labelled Sugar Concentration 0.18. Pour the sugar solution into the transparent container until the lens is just covered, as shown in Fig. 2.2. Check that v is still approximately 40 cm. u v sugar solution Fig. 2.2 • Adjust the position of the torch until it shows a sharp image of the LEDs on the screen. Measure and record the distances v and u. v = .......................................................... cm u = .......................................................... cm [1] (ii) Estimate the percentage uncertainty in your value of u. Show your working. percentage uncertainty = ......................................................% [1] (iii) • The combination of the lens and the sugar solution has a focal length f. Calculate f using the expression vu f = . (v + u) f = .......................................................... cm • The sugar solution has a refractive index n. Calculate n using the expression 0.553f n = . 1 + 0.333f n = ............................................................... [2] • Pour all the sugar solution back into the beaker labelled Sugar Concentration 0.18. (iv) Justify the number of significant figures you have given for your value of n. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a) Raw values for v to nearest mm and final value in range 39.0 to 41.0 cm. 1 2(a) Final value for u0 in range 4.0 to 6.0 cm. 1 2(b)(i) Raw values for u to nearest mm. 1 2(b)(ii) Absolute uncertainty of 0.5 to 1.0 cm and correct method of calculation to obtain percentage uncertainty in u. 1 If several readings have been taken, then the absolute uncertainty can be half the range, but not zero if values are equal. 2(b)(iii) Correct calculation of f 1 2(b)(iii) Correct calculation of n 1 2(b)(iv) Justification correctly linked to the significant figures in v and u 1 2(c) Second value of v 1 2(c) Second value of u 1 2(c) Quality: second u greater than first u 1 2(d) Two values of k calculated correctly 1 Final values of k are not written as fractions 2(e) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 20% 1 leading to a consistent conclusion. 2(f)(i) A Two k values are not enough to draw a valid conclusion 4 B Difficult to judge when image is sharpest / difficult to produce a sharp image C Difficult to hold torch in line with lens (axis) D Difficult to measure u (or v) due to parallax error / deciding lens position E Second solution may be diluted by traces of first solution / some of first solution remains on the lens F LEDs not at front of torch 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings and plot a graph / calculate more k values and compare 4 B Method to reduce unwanted light e.g. use screens around the area of the image / use darkroom C Mount torch on block (or stand) OR use an optical bench D Use set square next to rule (as pointer) / mark lens position on container E Clean the lens / clean the container / use a new container for second test F Remove glass from front of torch 1 mark for each point up to a maximum of 4.

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