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Cheat sheet · JEE Preparation Physics

Mechanical Properties of Solids cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Physics

Cheat sheet

Class 11 · Chapter 8Mechanical Properties of Solids

Stress ∝ strain within the elastic limit — Hooke's law.

1. Stress & Strain

Stress=FA\text{Stress} = \dfrac{F}{A}Strain=ΔLL\text{Strain} = \dfrac{\Delta L}{L}

Stress has units of N m⁻² (Pa); strain is dimensionless.

2. Elastic Moduli

ModulusFormulaApplies to
Young's (Y)F/AΔL/L\dfrac{F/A}{\Delta L/L}solids (length)
Bulk (B)−pΔV/V-\dfrac{p}{\Delta V/V}solids, liquids, gases
Shear (G)F/Aθ\dfrac{F/A}{\theta}solids only

Compressibility k=1/Bk = 1/B. Poisson's ratio = lateral strain / longitudinal strain.

3. Stress–Strain Curve

  • Proportional limit → elastic limit → yield point → ultimate stress → fracture.
  • Ductile: large plastic region (copper). Brittle: fracture soon after elastic limit (glass).
  • Elastomers (rubber) have no proportional region.

4. Energy Stored

U=12×stress×strain×volumeU = \tfrac12 \times \text{stress}\times\text{strain}\times\text{volume}

Applications: cranes' ropes, beams with I-section, bridges.

5. Key Points

  • Steel is more elastic than rubber (larger Y).
  • Y depends on material, not dimensions.
  • Shear modulus ≈ Y/3 for most solids.
  • Beam sag ∝ 1/(b d³): depth matters most.

Remember: Y, B, G | Hooke's law | stress–strain curve

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