Cambridge A Level Physics 9702 — 2025 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate the oscillations of a magnet. You have been provided with a small magnet attached to a string. You have also been provided with a bar magnet, a plotting compass and a sheet of paper. (a) • Draw a straight line of approximate length 20 cm on the sheet of paper. • Mark point X at the centre of this line as shown in Fig. 1.1. line X paper ≈ 20 cm Fig. 1.1 • Rotate the paper so that the straight line on the paper is aligned with the N–S direction shown by the plotting compass, as shown in Fig. 1.2. Keep the magnets away from the plotting compass while you are doing this. X plotting compass Fig. 1.2 • Fix the paper to the bench in this position using adhesive putty. The paper should stay in this position throughout the experiment. • Set up the apparatus as shown in Fig. 1.3. wooden rod boss stand string small magnet bench X h paper Fig. 1.3 • Adjust the position of the stand until the small magnet is directly over point X on the paper. • The distance between the bottom of the small magnet and the paper is h. Adjust the height of the boss until h is 3.0 cm. • Displace the small magnet through a short distance in the direction of the line on the paper. • Release the small magnet. The small magnet will oscillate. • The period of the oscillations of the small magnet is T0. Take measurements to determine T0. T0 = ......................................................... [2] (b) • Place the bar magnet on the sheet of paper at the position shown in Fig. 1.4. bar magnet line on paper X N N 10.0 cm Fig. 1.4 • Draw around the bar magnet. Do not move it from this position. • Displace the small magnet through a short distance in the direction of the line on the paper. Release the small magnet. The small magnet will oscillate. • The period of the oscillations of the small magnet is T. Record h and determine T. h = ............................................................... T = ............................................................... [1] (c) Write down your value of T0 from (a). T0 = ............................................................... Change the height of the boss such that h is in the range 3.0 cm ⩽ h ⩽ 9.0 cm. For each value of h, determine T. Repeat until you have six sets of values of h and T. Include your values from (b). T Record your results in a table. Include values of in your table. T0 [9] T (d) (i) Plot a graph of on the y‑axis against h on the x‑axis. [3] T0 (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 and h are related by the equation T = P h + Q T0 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]

Mark scheme: Question Answer Marks 1(a) Value of T0 in the range 1.0–1.4 s with unit. 1 At least two sets of nT where n ⩾ 5. 1 1(b) T ˂ T0. 1 1(c) Six sets of readings of h and time with correct trend (T increases as h increases) and without help from Supervisor scores 5 5 marks, five sets scores 4 marks etc. Range of h : hmin ⩽ 4.0 cm and hmax ⩾ 8.0 cm. 1 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. Consistency: All values of h must be given to the nearest mm. 1 Calculation: Correct calculation of T / T0. 1 1(d)(i) Axes: 1 Axes must be labelled with the correct 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, no awkward scales (e.g. 3:10 or fractions). Plotting of points: 1 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 x and y directions. Quality: 1 Trend of points must be positive. All points in the table (at least 5 points) must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within  5 mm (to scale) on the h-axis of all plotted points. 1(d)(ii) Line of best fit: 1 ‘Best fit’ is judged by the 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. Lines must not be kinked or thicker than half a square. Some candidates may choose to identify an anomalous point. If 6 or more points are plotted and 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. 1(d)(iii) Gradient: 1 The hypotenuse of the triangle used must 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. Method of calculation must be correct, not x / y. Gradient sign on answer line must be consistent with graph drawn. y-intercept: 1 Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line is substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. 1(e) P = candidate’s gradient value and Q = candidate’s intercept value. 1 Values must not be written as fractions or given to only one significant figure Units for P: cm–1 or m–1 consistent with readings 1 and no units for Q.

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2 In this experiment, you will investigate the behaviour of suspended cardboard sheets. You have been provided with two cardboard sheets labelled A and B. (a) • The thickness of sheet A is t. Use the micrometer to measure t. • Record t. t = .................................................. mm [1] (b) (i) • Use the nail to make holes in two corners of sheet A as shown in Fig. 2.1. holes sheet A Fig. 2.1 • Ensure that the sheet is able to swing freely on the nail when the nail is placed in either hole. • Set up the apparatus as shown in Fig. 2.2. boss nail held in boss sheet A string of plumb line stand bob bench Fig. 2.2 • Place the nail through one of the holes in A and place the string loop of the plumb line over the nail. • Draw a line on A along the length of the string of the plumb line. • Place the nail through the other hole in A and draw a line on A along the length of the string of the plumb line. • The two lines will cross at a point called the centre of gravity. Label this point P as shown in Fig. 2.3. P Fig. 2.3 • Use adhesive putty to attach the two 10 g masses to A at the edge of the sheet as shown in Fig. 2.4. x P mass m Fig. 2.4 • The distance between the top edge of the sheet and the centre of the masses is x, as shown in Fig. 2.4. The total mass attached to the sheet is m. Adjust the position of the masses until x is approximately 10 cm. • Record m and x. m = ............................................................ g x = ......................................................... cm [1] (ii) • Repeat the same process to determine the new centre of gravity of A. Label this point Q. • The distance between P and Q is y, as shown in Fig. 2.5. Q P y Fig. 2.5 Measure and record y. y = ................................................... cm [2] (iii) Estimate the percentage uncertainty in your value of y. Show your working. percentage uncertainty = ..................................................... % [1] y2 (iv) Calculate . m2 y2 = ............................................ cm2 g–2 [1] m2 y2 (v) Justify the number of significant figures that you have given for your value of . m2 ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a) All raw value(s) of t to the nearest 0.01 mm or all raw values to the nearest 0.001 mm 1 and final value in the range 0.80(0)–1.20(0) mm. 2(b)(i) All raw x to the nearest mm and final value of x in the range 9.5–10.5 cm. 1 2(b)(ii) Raw value of y to the nearest mm. 1 Value of y in the range 3.0–5.0 cm. 1 2(b)(iii) Percentage uncertainty based on absolute uncertainty in y in range 2–5 mm. 1 Correct method of calculation to find percentage uncertainty. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. 2(b)(iv) Correct calculation of y2 / m2. 1 2(b)(v) Justification for significant figures in y2 / m2 linked to significant figures in y and m only. 1 2(c) Second values of t, m and x. 1 Second value of y. 1 Second value of y > first value of y. 1 2(d) Two values of k calculated correctly. 1 The final k values must not be written as fractions or given to only one significant figure. 2(e) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 20%, leading to a consistent conclusion. 2(f)(i) A Two (sets of) readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few 4 readings”). B Difficult to draw lines with a reason e.g. because card is hanging / card or string moves when line being made / card not vertical. C Mass of putty not taken into account. D Difficulty in measuring x with a reason e.g. judging centre of the mass / placing the centre of the mass where required / mass covers up the mark made for x. E Difficulty in locating centre of gravity or difficulty in accuracy of y with a reason e.g. string is too thick / card sticks on the nail / nail is too thick. 1 mark for each point up to a maximum of 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). 4 B Make a mark and then take off and draw line on the card on the bench or clamp rule vertically. C Measure mass of putty and add to the masses / measure the total mass of the masses and the putty or use a specified lighter adhesive e.g. tape or glue. D Measure to near and far side and average for x. E Use thinner string / thinner nail / use a pin / make hole bigger or smoother. 1 mark for each point up to a maximum of 4.

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