Cambridge A Level Physics 9702 — 2025 May/June Paper 5 · Variant 2

1 A thin solid disc of radius r and thickness z is attached to a thin axle. String is wrapped around the axle, as shown in Fig. 1.1. z disc axle r string block Fig. 1.1 A block of mass m is attached to the string. The block is released from rest and falls downwards. The block has speed v when it has fallen through a distance h from the point of release. The value of v is determined using one light gate connected to a timer. It is suggested that v is related to m by the relationship h πr 2z 1 = + v 2 2PQm P where P and Q are constants. Plan a laboratory experiment to test the relationship between v and m. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for P and Q. In your plan you should include: • the procedure to be followed • the measurements to be taken • the control of variables • the analysis of the data • any safety precautions to be taken. 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Mark scheme: Question Answer Marks 1 Defining the problem vary m and measure v or m is the independent variable and v is the dependent variable 1 keep h constant 1 Methods of data collection labelled diagram of workable experiment including: 1 • axle resting on support(s) (on stands) • supports placed on bench • light gate (connected to timer) positioned at a distance h • light gate labelled and h indicated vertical metre rule clamped to a stand in a position close to block to measure h 1 method to determine v using an interrupt length, e.g. v = length of block / time recorded by the timer 1 method to measure m, e.g. use a (top-pan) balance 1 Method of analysis 1 1 1 plot a graph of against or equivalent v 2 m Do not accept logarithms. 1 1 1 1 1 1 against against v 2 m m v 2 1 gradient P = P = − h  y -intercept y -intercept  h or r 2 z  gradient P = 2Qh 1 1 1 1 1 against against v 2 m m v 2 r 2 z r 2 z  y -intercept Q = Q = − 2Ph  gradient 2 or r 2 z  y -intercept Q = 2  gradient Additional detail including safety considerations 6 D1 precaution linked to falling block resulting in damage to block / bench, e.g. use a cushion / sand tray to prevent damage to bench or precaution linked to stands falling, e.g. clamp stand(s) to the bench prevent stand falling D2 keep r and z constant D3 method to determine r e.g. use calipers / ruler to measure diameter d and r = d / 2 D4 measure z with a micrometer / calipers 1 D5 set square correctly positioned between rule and bench to ensure that rule to measure h is vertical D6 method to keep h constant by identifying constant initial position of the bottom of the block, e.g. clamped pin / rod to indicate the starting point each time or (fiducial) marker on rule D7 description of method to ensure that axle can rotate, e.g. axle is lubricated at the supports to enable axle to rotate, axle is not fixed at the supports so axle can rotate D8 use a large length of block to reduce (percentage) uncertainty in interrupt time or increase the time light gate is interrupted D9 repeat experiment for the same value of m and determine the average v 1 D10 relationship valid if a straight line is produced (with y-intercept = ). hP Do not accept line passing through the origin.

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2 A student investigates a circuit containing capacitors. The circuit is connected with a capacitor of capacitance A, as shown in Fig. 2.1. X A Y P Q V Z Fig. 2.1 Two capacitors, each of capacitance C, are connected in parallel between P and Q. Initially, switch X and switch Z are closed and switch Y is open. Switches X and Z are opened. Switch Y is then closed. The maximum potential difference between P and Q is measured using the voltmeter. This procedure is repeated and the mean maximum potential difference V between P and Q is determined. The experiment is then repeated by changing the number n of capacitors, each of capacitance C, connected in parallel between P and Q. It is suggested that V and n are related by the equation EA = V(nC + A) where E is the electromotive force (e.m.f.) of the battery. 1 (a) A graph is plotted of on the y-axis against n on the x-axis. V Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of n and the two measured values of the maximum potential difference V1 and V2 are given in Table 2.1. Table 2.1 1 n V1 / V V2 / V V / V / V–1 V 2 4.30 4.20 3 3.65 3.75 4 3.30 3.20 5 2.85 2.95 6 2.65 2.55 7 2.30 2.40 1 Calculate and record values of V / V and / V–1 in Table 2.1. Include the absolute uncertainties 1 V in V and . [2] V 1 1(c) (i) Plot a graph of / V–1 against n. Include error bars for . [2] V V (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = .......................................................... [2]

Mark scheme: 2(a) C 1 gradient = EA 1 y-intercept = E 2(b) 1 1 V / V / V–1 V 4.25 0.235 or 0.2353 3.70 0.270 or 0.2703 3.25 0.308 or 0.3077 2.90 0.345 or 0.3448 2.60 0.385 or 0.3846 2.35 0.426 or 0.4255 1 Values of V / V and / V–1 correct as shown above. V Uncertainties in V all  0.05 1 and 1 uncertainties in from  0.002 or  0.003 increasing to  0.009. V 2(c)(i) Six points from (b) plotted correctly. 1 Must be within half a small square. Diameter of points must be less than half a small square. 1 1 Error bars in plotted correctly. V All error bars must be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 2(c)(ii) Straight line of best fit drawn. 1 Thickness of the line must be less than half a small square. Do not accept line from top point to bottom point. Line must pass between (2.65, 0.26) and (2.80, 0.26) and between (6.30, 0.40) and (6.50, 0.40). Worst acceptable straight line drawn (steepest or shallowest possible line that passes through all the error bars). 1 Thickness of the line must be less than half a small square. All error bars must be plotted. 2(c)(iii) Gradient determined with clear substitution of data points into y / x. 1 Distance between data points must be greater than half the length of the drawn line. Gradient determined of worst acceptable line with clear substitution of data points into y / x. 1 uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 2(c)(iv) y-intercept determined by substitution of correct point into y = mx + c. 1 y-intercept of worst acceptable line determined by substitution into y = mx + c. 1 uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) Do not accept ECF from false origin method. 2(d)(i) E determined using y-intercept and E and C given to 2 or 3 significant figures. 1 1 E = y -intercept C determined using gradient and E and C given with correct units with appropriate powers of ten. 1 A  gradient C = or C = A  E gradient y -intercept unit of E: V unit of C: F 2(d)(ii) Percentage uncertainty determined with method shown. 1  A gradient y -intercept  C % =  + +   100  A gradient y -intercept  or  A gradient E  C % =  + +   100 with method to determine E shown  A gradient E  2(e) V determined to a minimum of 2 significant figures from (c)(iii) and (c)(iv) or (d)(i) with correct substitution. 1 1 V = 10  gradient+y -intercept or EA V = 10C + A

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