AQA AS Level Physics Paper 2, June 2023: Question 1

10 marks · Medium difficulty · Practical Techniques & Data Analysis

Analyze a series of practical measurements involving a micrometer screw gauge, percentage uncertainties, stationary waves on a wire, and data analysis of frequency versus wire diameter.

Practise this question

Question

Question text

01.1 Figure 1 shows a micrometer screw gauge.

Figure 1

What is the reading on the micrometer?

Tick ( ) one box.

[1 mark]

6.25

6.75

7.25

8.25 3

01.2 A metal wire of diameter d is held in the gap between the anvil and the spindle.

Just before the reading of d is taken, the gap is closed using the ratchet and not the

thimble.

*02* Explain why the gap is closed in this way.

[1 mark]

01.3 The mass per unit length μ of the metal wire is given by

πρd 2

μ =

where ρ is the density of the metal.

Values of d and μ are used to calculate ρ.

The percentage uncertainty in d is 1.2%.

The percentage uncertainty in μ is 2.0%.

Calculate the percentage uncertainty in the result for ρ.

[2 marks]

percentage uncertainty = %

Figure 2 shows apparatus used to investigate how the frequency of stationary waves

on a wire depends on its diameter d.

Figure 2

When the signal generator is switched on, the horizontal part of the wire oscillates.

A student changes the frequency until the first-harmonic stationary wave is produced.

The student records the frequency f of the first harmonic and then turns off the signal

generator.

She removes the wire and measures d using a micrometer.

She then repeats the experiment for wires of different diameter.

01.4 The wires used in the experiment are made of the same metal so that ρ is a control

variable.

State two other control variables in the experiment.

[2 marks]

Figure 3 is a plot of the experimental data.

Figure 3

01.5 1

The student suggests that f ∝ .

Deduce, using data points from Figure 3, whether this suggestion is correct.

[2 marks]

01.6 Another student repeats the experiment with the mass of M doubled.

Explain how this student’s plotted data compare with Figure 3.

[2 marks]

Mark scheme

Show the mark scheme

Question Answers Additional Comments/Guidance Mark AO

01.1 6.75 CAO 1 AO3

01.2 any sensible answer describing possible consequences of use Accept ‘the frame of the micrometer might become 1 AO1

of the thimble, e.g. can cause the wire to be warped’ / ‘damage might occur to the screw thread

distorted/damaged; or reduces the diameter. mechanism’ / ‘may lead to the reading shown being

smaller than true value’

Condone ‘squeezed’. Condone ‘change diameter’.

Reject ‘might change the reading’, ‘affect results’,

‘cause a reading below zero’, ‘could lead to

systematic error’, ‘over-tighten’ or ‘holds wire more

securely’.

01.3 fully correct calculation 1 2 ((2 × 1.2%) + 2.0% =) 4.4% 1 2 2 AO2

OR For 12 allow any of (2 × 1.2%) OR 2.4% OR 1.2%

+ 2.0% OR 3.2% OR 1.44% + 2.0% OR 3.4% seen

partly correct calculation 12 in working.

For 1 mark condone misreading leading to ‘(2 ×

2.0%) + 1.2% = 5.2%’ OR ‘4% + 1.2% = 5.2%’.

01.4 length of wire between oscillator and pulley 1 For 1 allow ‘distance between oscillator and 2 AO3

pulley’ or ‘length of horizontal/oscillating wire’ or

mass of M 2 use of annotation to Figure 2 to identify correct

dimension with a symbol, eg L.

For 1 ‘length of wire’ is insufficient.

For 2 allow ‘weight of M’ or ‘suspended mass’.

For 2 accept ‘tension in wire’.

Reject bland ‘M’ or ‘the mass’ or ‘tension’.

Treat ‘mass per unit length of wire’ as neutral.

01.5 calculates d × f at least twice 1 2 AO3

d / mm f / Hz (d × f ) / mm s–1

states how their calculations support a conclusion that f is

inversely proportional to d 2 0.85 28.5 24.2 (24.23)

0.68 36.0 24.5 (24.48)

0.54 44.5 24.0 (24.03)

0.44 55.5 24.4 (24.42)

0.37 65.0 24.1 (24.05)

Allow reverse working or use of readings from a line

of best-fit.

For 1 condone misreading of scale of one axis, or

one misreading.

For 2 apply list principle to calculations i.e. for 2 or

3 calculations, all must be correct; for 4

calculations, condone 1 error; for 5 calculations,

condone 2 errors.

Do not allow 1 sf for constant of proportionality.

01.6 For 1 allow (all) points / line / graph move(s) up. 2 AO3

f values increase 1

Must not imply d changes OR points / line moves

by √2 2 right OR that μ changes.

8 Treat ‘graph is stretched upwards / in the y-

direction’ as neutral.

Total 10

How to answer it

Micrometer Readings, Experimental Uncertainties & Stationary Waves

What this question tests

This multi-part practical physics question tests your ability to read precision measuring instruments (micrometers), understand standard laboratory techniques to prevent systematic errors, combine percentage uncertainties, identify control variables in wave experiments, analyse graphical data to test inverse proportionality, and predict how altering experimental parameters impacts functional relationships.

Question 01.1 [1 mark]

Reading a Micrometer Screw Gauge

✅ Correct Answer

6.75 mm (Ticked)

💡 Key Knowledge

Main scale reveals visible graduations past 6 mm (shows 6.5 mm mark below the datum line).
Micrometer scale aligns at the 25 mark with the central reference line.
Total reading = Main scale reading + (Thimble reading × 0.01 mm) = 6.5 mm + 0.25 mm = 6.75 mm.

Mark scheme guidance: 1 mark for CAO (Correct Answer Only).

Question 01.2 [1 mark]

Experimental Technique: Using the Ratchet

✅ Correct Answer

The ratchet slips when sufficient force is applied, preventing excessive force that could distort/damage the wire, warp the micrometer frame, or damage the screw thread mechanism (leading to an artificially reduced diameter reading).

❌ Common Errors

Vague statements like "to avoid human error", "to make it accurate", or "to not over-tighten" without stating the physical consequence (wire distortion or frame warping) do not score.

Examiner commentary: Top-level responses explicitly tied closing via the ratchet to preventing plastic deformation of the wire or mechanical warping of the spindle tool.

Question 01.3 [2 marks]

Combining Percentage Uncertainties

📐 Step-by-Step Calculation

Given formula: μ = (π ρ d²) / 4 , rearranged for ρ = (4μ) / (π d²) .
Identify powers: ρ depends directly on μ (power 1) and inversely on d² (power 2).
Apply uncertainty rules (add percentage uncertainties when multiplying/dividing, multiply percentage uncertainty by power for exponents):
% uncertainty in ρ = % uncertainty in μ + (2 × % uncertainty in d)
Substitute values: 2.0% + (2 × 1.2%) = 2.0% + 2.4% = 4.4%

🧠 Exam Technique

Always show your substitution explicitly. Writing 2 × 1.2% + 2.0% = 4.4% guarantees the method mark even if an arithmetic slip happens elsewhere.

Mark breakdown: 1 mark for identifying the correct combination (2 × 1.2%) + 2.0% ; 1 mark for final answer of 4.4%.

Question 01.4 [2 marks]

Identifying Control Variables

💡 Key Knowledge & Accepted Answers

To keep wave frequency consistent across trials for varying diameters, other factors affecting string wave speed must remain constant:

1. Length of the wire between the mechanical oscillator and the fixed pulley (or distance between nodes).
2. Mass of the suspended mass M (or tension in the wire).

❌ Common Errors

Writing just "length" or "mass" is too vague. You must specify length of the wire between bridges/supports and mass hung over the pulley (tension).

Mark scheme guidance: 1 mark for each valid control variable specified clearly.

Question 01.5 [2 marks]

Data Analysis: Inverse Proportionality

📐 Step-by-Step Calculation

Test inverse proportionality ( f ∝ 1/d ) by checking if the product f × d is approximately constant.
Pick at least two coordinate pairs from Figure 3:
- At d = 0.85 mm, f = 28.5 Hz → 0.85 × 28.5 = 24.2 mm Hz
- At d = 0.44 mm, f = 55.5 Hz → 0.44 × 55.5 = 24.4 mm Hz
Conclusion: Since the calculated products are nearly constant (constant of proportionality ≈ 24 mm Hz), the student's suggestion is correct.

🧠 Exam Technique

To secure both marks, you must show explicit numerical calculations (at least two points tested) AND make a clear concluding statement linking the constant product to inverse proportionality.

Mark breakdown: 1 mark for calculating d × f for at least two points; 1 mark for stating how consistency supports inverse proportionality.

Question 01.6 [2 marks]

Predicting Graph Modifications

✅ Correct Answer

Frequency values ( f ) increase (1 mark).
The increase factor is √2 or approximately 1.41 times higher for every corresponding diameter value (1 mark).

💡 Underlying Physics

The speed of a transverse wave on a string is given by v = √(T/μ) = √(Mg/μ) . Since μ = πρd²/4 , the first harmonic frequency is f = v/(2L) . Doubling mass M multiplies the tension by 2, which scales wave speed and frequency by √2 .

Mark breakdown: 1 mark for indicating the points/line move upwards; 1 mark for quantifying the scale shift as √2 .

Topics

Physics · Practical skills · Required Practicals · 3.1 Measurements and their errors · 3.3 Waves · Experimental design · Data analysis · Uncertainty and evaluation · AS practicals (1–6)

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.