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Elasticity formula sheet

Every formula in the Elasticity chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 27 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Stress, strain and Hooke's law

Stress
6× asked, last 2025
stress=FA(N m−2=Pa)\text{stress}=\frac FA\quad(\text{N m}^{-2}=\text{Pa})
Normal (tensile or compressive) or shear (force along AA). A=πr2=πd2/4A=\pi r^2=\pi d^2/4; hollow: π(r22−r12)\pi(r_2^2-r_1^2).
Strain
2× asked, last 2024
ΔLL (longitudinal),ΔVV (volume)θ≈Δxh (shear)\begin{aligned}&\frac{\Delta L}L\ (\text{longitudinal}),\qquad \frac{\Delta V}V\ (\text{volume})\\&\theta\approx\frac{\Delta x}h\ (\text{shear})\end{aligned}
No unit; shear strain is the tilt angle in radians.
Hooke's law
4× asked, last 2024
stress=E×strain\text{stress}=E\times\text{strain}
Up to the proportional limit. A modulus depends only on the material and temperature.
Stress–strain curve
1× asked, last 2023
Y=slope (straight part),u=area under the curveY=\text{slope (straight part)},\qquad u=\text{area under the curve}
Proportional limit → elastic limit → yield → ultimate stress → fracture. Ductile: long plastic part.

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Practise Elasticity

23 more formulas in 5 topics

Young's modulus and stretched wires, Bulk modulus and compressibility, Shear modulus and Poisson's ratio, Elastic potential energy and Thermal stress. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Young's modulus and stretched wires

  • Extension of a wire16×
  • Comparing two wires10×
  • Natural length from two loads7×
  • Find the tension first11×
  • Wire sagging under a central load
  • Wires in series2×
  • Rod hanging under its own weight2×
  • Rod rotating about one end
  • Breaking stress4×
  • Searle's experiment3×
  • Sag of a beam loaded at its centre

Bulk modulus and compressibility

  • Bulk modulus12×
  • Compression at a depth5×
  • Density and side under pressure3×
  • Bulk modulus of a gas1×

Shear modulus and Poisson's ratio

  • Modulus of rigidity3×
  • Poisson's ratio1×
  • Volume change of a stretched wire
  • Relations between the moduli2×

Elastic potential energy

  • Energy stored in a stretched wire2×
  • Energy density5×

Thermal stress

  • Rod between rigid supports4×
  • Wave speed in a rod or fluid

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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