Cambridge A Level Physics 9702 — 2025 Oct/Nov Paper 5 · Variant 1

1 On a bench, a steel ball of radius r is used to compress a spring by a distance x. The ball is held at rest in this position, as shown in Fig. 1.1. compressed spring ball bench P Fig. 1.1 The ball is released and rolls along the bench. At a fixed point P, the ball has speed v. The speed of the ball at P is determined using one light gate connected to a timer. Several steel balls of different radii are available. It is suggested that v is related to r by the relationship Ykx2 v 2 = r nρ where k is the spring constant of the spring, ρ is the density of the steel, and Y and n are constants. Plan a laboratory experiment to test the relationship between v and r. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for Y and n. 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. Diagram .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .......................................................................................................................................................... [15]

Mark scheme: Question Answer Marks 1 Defining the problem vary r and measure v or r is the independent variable and v is the dependent variable 1 keep x constant 1 Methods of data collection labelled diagram of workable experiment including: 1 • one end of spring resting against block clamped to bench using G-clamp • light gate positioned at P • light gate connected to timer • apparatus shown on bench • labels for light gate and P and at least one other label from bench, block, stand, spring, ball, timer method to determine r, e.g. use calipers or micrometer to measure diameter d and r = d / 2 1 description of method to determine v, use diameter of ball (to interrupt beam) ÷ measured time at light gate positioned at P 1 instrument to determine x, e.g. rule(r) or calipers 1 Method of Analysis plot a graph of (2 lg v) or (lg v2) against lg r 1 or plot a graph of (lg v) against (lg r) or equivalent, e.g. (ln v) against (ln r) n = −gradient for (2 lg v) or (lg v2) against lg r 1 or n = −2 gradient for (lg v) against lg r 1  10y -intercept 1 Y = for (2 lg v) or (lg v2) against lg r kx 2 or  10 2 y -intercept Y = for (lg v) against lg r kx 2 Additional detail including safety considerations 6 D1 precaution to prevent ball leaving bench, e.g. screens around apparatus / cushions on bench (to stop the ball) D2 keep k and constant D3 description of method to determine k, e.g. add mass to spring and k = mg / extension or use newton meter to measure force applied to spring and k = force / extension or take several readings of force and extension, plot a force–extension graph and k = gradient m D4 description of experimental method to determine , e.g. measure mass of ball using a balance and = 4 3 r 3 D5 repeat measurements of diameter or d in different directions and determine the average value of d D6 method to keep x constant, e.g. use a pin / ruler / card to indicate the starting point each time to keep x constant D7 x = original length of spring – compressed length of spring D8 adjust (vertical) position of light gate so that the diameter of (each) ball cuts the beam D9 repeat experiment for the same value of r and determine the average v 1  Ykx 2  1  Ykx 2  D10 relationship valid if a straight line is produced (with y-intercept = lg   or lg   ).  2      Do not accept line through the origin.

More questions on Physical quantities

2 A student investigates light from different galaxies. Fig. 2.1 shows the lines in the absorption spectrum from a distant galaxy. λ increasing wavelength Fig. 2.1 The wavelength of one of the lines in the absorption spectrum is λ. The wavelength of this spectral line in the laboratory is λ0. The observations of the same spectral line are repeated for different galaxies. The student determines the distance d of each galaxy from the Earth. It is suggested that λ and d are related by the equation λ – λ0 Hd = λ0 c where c is the speed of light in free space and H is the Hubble constant. d (a) A graph is plotted of λ on the y-axis against on the x-axis. c Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of d and λ are given in Table 2.1. Table 2.1 d d / 1021 km / 1015 s λ/ nm c 0.48 ± 0.12 658.4 1.04 ± 0.12 661.2 1.45 ± 0.12 664.2 1.80 ± 0.12 665.7 2.85 ± 0.12 672.4 3.75 ± 0.12 678.2 The value of c is 3.00 × 105 km s–1. d d Calculate and record values of / 1015 s in Table 2.1. Include the absolute uncertainties in . c c [2] d d (c) (i) Plot a graph of λ/ nm against / 1015 s. Include error bars for . [2] c c (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) gradient = H0 1 y-intercept = 0 2(b) 1 d / 1015 s c (1.6 or 1.60)  0.40 (3.47 or 3.467)  0.40 (4.83 or 4.833)  0.40 (6.00 or 6.000)  0.40 (9.50 or 9.500)  0.40 (12.5 or 12.50)  0.40 d Values of correct as shown above. c d 1 Uncertainties in correct as shown above. c 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. d 1 Error bars in plotted correctly. c 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 (2.5, 660.0) and (2.9, 660.0) and between (11.2, 676.0) and (11.6, 676.0). Worst acceptable 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 with consistent power of ten in m and x and y 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) 0 determined using y-intercept and 0 given to 3 or 4 significant figures and H given to 2, 3 or 4 significant figures. 1 0 = y-intercept H determined using gradient and 0 and H given with SI units with appropriate powers of ten. 1 gradient gradient H = or H = y -intercept 0 Unit of 0: m, nm, m Unit of H: s−1 2(e) Value of T determined to a minimum of two significant figures from (d) and correct power of ten. 1 1 T = H Absolute uncertainty determined with correct substitution. 1  y -intercept gradient  T =  +   T  y -intercept gradient  or  max 0   max y -intercept  T =   − T or T =   − T  min gradient   min gradient  or  min 0   min y -intercept  T =   − T or T =   − T  max gradient   max gradient 

More questions on Hubble’s law and the Big Bang theory