Class 11 Physics · NCERT notes for NEET

Mechanical Properties of Solids: NCERT Notes, Formulas and Tricks for NEET

How solids stretch, shear and squeeze under forces: stress, strain, Hooke's law, the stress-strain curve, the three elastic moduli and stored elastic energy. It is a short chapter; NEET usually asks one formula-based question from it, often a Young's modulus ratio for wires.

• 1. Stress, strain and Hooke's law
• 2. Elastic moduli 🔒
• 3. Elastic potential energy 🔒

Topic 1 is open for everyone. The full chapter, quick revision and practice open with a plan, or start free with 5 full chapters.

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Topic 1

Stress, strain and Hooke's law

A steel rod only 2 cm thick can hold up about 30 tonnes, yet stretches by less than a millimetre per metre. Stress and strain tell you why.

• Elasticity: a body regains its original size and shape when the deforming force is removed. Plasticity: it stays permanently deformed (putty, mud). No real material is perfectly elastic or perfectly plastic.
• Atomic picture: atoms sit in stable equilibrium under interatomic forces. Deforming the body changes their spacing, and these forces pull them back, giving the restoring force.
• Stress = restoring force per unit area, $\sigma =F/A$. SI unit $\mathrm{N}{\mathrm{m}}^{-2}$ = pascal (Pa), dimensions $[M{L}^{-1}{T}^{-2}]$, same as pressure.
• Three kinds of stress: longitudinal (tensile or compressive, force normal to the face), shearing (force tangential to the face) and hydraulic (equal normal pressure from all sides).
• Strain = change in dimension / original dimension, so it has no unit and no dimensions. Longitudinal $\Delta L/L$, shear $\Delta x/L=\tan \theta \approx \theta$, volume $\Delta V/V$.
• Hooke's law: for small deformations stress $\propto$ strain, i.e. stress $=k\times$ strain, where $k$ is the modulus of elasticity.
• Stress-strain curve of a metal: straight up to the proportional limit A (Hooke's law region); the body still recovers fully up to the yield point B (elastic limit), whose stress is the yield strength ${\sigma }_y$.
• Beyond B the strain rises fast for little extra stress. Unloaded at C, the wire does not return to zero: the leftover strain is the permanent set (plastic deformation).
• D is the ultimate tensile strength (maximum stress); after D the wire thins and breaks at E (fracture). Ductile: D and E far apart (copper, aluminium). Brittle: D and E close (glass, cast iron).
• Elastomers such as rubber and the elastic tissue of the aorta stretch to huge strains and still recover, but their curve has no straight part, so Hooke's law does not hold.

Formulas

• $\sigma =\frac{F}{A}$
  Stress; Pa, $[M{L}^{-1}{T}^{-2}]$
• $\epsilon =\frac{\Delta L}{L}$
  Longitudinal (tensile or compressive) strain
• $\text{shear strain}=\frac{\Delta x}{L}=\tan \theta \approx \theta$
  $\theta$ in radians, small angle
• $\text{volume strain}=\frac{\Delta V}{V}$
  Under hydraulic stress
• $\text{stress}=\text{modulus}\times \text{strain}$
  Hooke's law, valid only in the linear region

Tips, tricks and hacks

Common mistakes

NEET traps

"Hooke's law holds up to the elastic limit" looks right but NCERT says up to the proportional limit (the linear part).

Strain has no unit, but shear strain is an angle in radians; NEET may give $\theta$ in degrees and expect you to convert.

Stress is the internal restoring force per area; it has the same unit as pressure but is not a vector, so do not add stresses like vectors.

Practise Mechanical Properties of Solids questions

Topic-wise practice from Level 1 to Level 3, NCERT-based questions and NEET PYQs, with a full solution after every answer.