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Solids

Young's modulus, stress and strain, and the elastic energy of a stretched wire. Almost every question is a calculation.

Questions in the bank
78
q/paper in 2025–26
0.57
Numeric answer
42%
Notes pages
4

Tier: Long tail

When you’ll see it

A wire stretched by a load, two wires compared, a breaking load, a body squeezed under pressure or sheared, or the energy stored in a stretched wire.

How this chapter is tested

Most questions rest on one relation, ΔL = FL/(AY), and on its versions for volume and shape. The work is finding the tension a wire really carries and seeing which length, area or modulus the question has changed.

Ratio questions dominate: a diameter ratio becomes an area ratio by squaring, and a wire drawn out at fixed volume changes its length and its area together. Many are set as numeric-answer questions.

This is a long-tail chapter. Marks are lost on units (mm² and cm² against m²), on a diameter used as a radius, on giving a wire pulled from both ends twice its tension, and on testing only the upper wire of a stack for breaking.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Stress, strain and Young's modulus

    ΔL = FL/(AY) with A = πd²/4; Y belongs to the material, and on a strain–stress graph the slope is 1/Y.

  • Loaded wires and breaking stress

    Find each wire's tension first: equal in series, everything below it in a stack, from a force balance when the load accelerates or swings.

  • Bulk modulus, shear and Poisson's ratio

    B = ΔP/(ΔV/V), η = (F/A)/θ, and Y = 2η(1 + σ) = 3B(1 − 2σ) tie the moduli together.

  • Hooke's law and stored energy

    T = k(l − l₀) gives the natural length from two readings; a stretched wire stores ½FΔL, or ½ × stress × strain per unit volume.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Pulled from both ends taken as 2F

    Two people pulling the ends with F each give a tension F, the same as a wall at one end. Using 2F doubles the answer.

  • A diameter used as a radius

    A = πd²/4. Putting d into πr² makes the area four times too large and the extension four times too small.

  • Only the upper wire tested

    The upper wire carries more but is often thicker. Test every wire against its own breaking stress.

  • The load's work taken as the stored energy

    A load that stretches a wire by ΔL loses mgΔL, but the wire stores only ½mgΔL; the rest leaves as heat or oscillation.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Solids notes

Drill every Solids question

78 questions from the bank, across 4 subtopics.

Drill the 78 questions

Drill one subtopic at a time

The 4 subtopics, in teaching order.

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