Physics 9702/53 October/November 2025: question paper and mark scheme
Cambridge AS & A Level Physics (9702), Paper 5 Planning, Analysis and Evaluation, October/November 2025. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
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 v2 = 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.
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Diagram
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…… [15]
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5
Mark scheme
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 ρ × 10 y -intercept 1
Y= for (2 lg v) or (lg v2) against lg r
kx 2
or
ρ × 102×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 ρ 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 ρ, e.g. measure mass of ball using a balance and ρ =
4 3
πr
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 ).
ρ 2 ρ
Do not accept line through the origin.
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]
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(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]
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7
680
678
676
λ / nm
674
672
670
668
666
664
662
660
658
0 2 4 6 8 10 12 14 d
/ 1015 s c
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8
(iv) Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer.
y-intercept = …… [2]
(d) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of λ0 and H. Include appropriate units.
λ0 = ……
H = ……
[2]
(e) Hubble’s law suggests that the age T of the universe is related to H by
1
T= .
H
Determine a value for T. Include the absolute uncertainty in your answer.
T = …… s [2]
[Total: 15]
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series.
Mark scheme
2(a) gradient = Hλ0 1
y-intercept = λ0
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 Δy / Δx. 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 Δy / Δx. 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) λ0 determined using y-intercept and λ0 given to 3 or 4 significant figures and H given to 2, 3 or 4 significant figures. 1
λ0 = y-intercept
H determined using gradient and λ0 and H given with SI units with appropriate powers of ten. 1
gradient gradient
H= or H =
y -intercept λ0
Unit of λ0: m, nm, μm
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
Δy -intercept Δgradient
ΔT = + ×T
y -intercept gradient
or
max λ0 max y -intercept
ΔT = − T or ΔT = −T
min gradient min gradient
or
min λ0 min y -intercept
ΔT = − T or ΔT = −T
max gradient max gradient
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On this page, free: the mark scheme for AS & A Level Physics 9702/53, October/November 2025 (9702_w25_ms_53), and the question paper (9702_w25_qp_53), to read or download, with each question's marking points written out underneath.
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Physics 9702/53 for October/November 2025 is out of 30 marks, with 1 hour 15 minutes to answer it.
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