Physics 9702 · syllabus 6
Cambridge A Level Physics 9702 — Deformation of solids topical past papers
How solids stretch and compress under load: Hooke's law, stress, strain and the Young modulus, elastic and plastic behaviour, and stored elastic energy.
- Questions
- 325
- Years
- 2009–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 101
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What Deformation of solids covers
Tensile forces stretch a material and compressive forces squash it; in this course both act along one line. Up to the limit of proportionality, extension is proportional to load, which is Hooke's law, and the spring constant k = F/x describes how stiff a particular spring or wire is. But k depends on the sample's size, so to describe the material itself you use stress, force per unit cross-sectional area, and strain, extension per unit original length.
The Young modulus is stress divided by strain, measured in pascals. You should be able to describe measuring it for a metal wire: a long wire, a micrometer for the diameter at several points, a scale or vernier to measure the extension as loads are added, and a graph of stress against strain whose gradient in the straight region gives the modulus.
Beyond the elastic limit the deformation is plastic, and the material does not return to its original shape when the load is removed. The area under a force–extension graph is the work done in deforming it; within the limit of proportionality this stored elastic potential energy is ½Fx = ½kx². This is AS content, examined on Papers 1 and 2, and it uses the energy ideas of the previous topic.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- 6 Deformation of solids
- 6.1 Stress and strain
- 6.2 Elastic and plastic behaviour
What you should be able to do
- Use Hooke's law and k = F/x, and identify the limit of proportionality on a force–extension graph
- Define and calculate stress, strain and the Young modulus
- Describe an experiment to measure the Young modulus of a metal wire, including how to reduce uncertainty
- Distinguish elastic from plastic deformation, and the limit of proportionality from the elastic limit
- Find the work done or elastic potential energy from the area under a force–extension graph
Key ideas
- Hooke's law F = kx, with the spring constant k in N m⁻¹
- Stress σ = F/A (Pa); strain ε = x/L (no unit)
- Young modulus E = σ/ε = FL/(Ax) (Pa)
- Elastic potential energy Eₚ = ½Fx = ½kx², valid up to the limit of proportionality
How Deformation of solids has been examined
From 2022 to 2026, Deformation of solids was on Paper 2 · AS Level Structured Questions in 8 of 11 exam series, worth about 10% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Multiple Choice | 80 | 6% | 10 of 11 |
| Paper 2 · AS Level Structured Questions | 21 | 10% | 8 of 11 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 1.
Filed in Momentum under: Deformation of Solids.
A worked example
A steel wire of original length 2.00 m and diameter 0.40 mm extends by 4.0 mm when a load of 50.0 N hangs from it. Assuming the limit of proportionality is not passed, find the Young modulus of the steel and the energy stored in the wire.
- Cross-sectional area: A = π(0.20 × 10⁻³)² = 1.26 × 10⁻⁷ m²
- Stress = F/A = 50.0 / 1.257 × 10⁻⁷ = 3.98 × 10⁸ Pa
- Strain = x/L = 4.0 × 10⁻³ / 2.00 = 2.0 × 10⁻³
- Young modulus = stress ÷ strain = 3.98 × 10⁸ / 2.0 × 10⁻³ = 1.99 × 10¹¹ Pa
- Energy stored = ½Fx = ½ × 50.0 × 4.0 × 10⁻³ = 0.10 J
Answer: Young modulus 2.0 × 10¹¹ Pa; energy stored 0.10 J
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Using the diameter where the radius belongs in A = πr² — the area comes out four times too large and the Young modulus four times too small
- Leaving the extension in millimetres while the length is in metres — strain needs the same unit top and bottom, or the modulus is wrong by a factor of 1000
- Treating the limit of proportionality and the elastic limit as the same point — beyond the first the graph curves, but the wire can still return to its original length until the second is passed
- Using ½Fx for the energy stored once the graph has curved — beyond the limit of proportionality you need the actual area under the curve, for example by counting squares
Exam technique
- When describing the Young modulus experiment, name each instrument with the quantity it measures, and say you repeat the diameter reading at several points and in different directions
- Take the gradient of a stress–strain graph only from its straight-line region, and say so
- Keep strain as a number such as 2.0 × 10⁻³ rather than a percentage when substituting into E = σ/ε
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.