Elasticity formulas

Every formula JEE Advanced expects you to know for Elasticity, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 22
Subject: Physics
Exam: JEE Advanced
No sign-in needed: ₹0

Elasticity, every formula

22 formulas, typeset and free. Print it, or keep it open beside your practice.

Stress
$stress = \frac{F}{A}$
Longitudinal strain
$strain = \frac{Δ L}{L}$
Hooke's law
$stress \propto strain$
within elastic limit
Young's modulus
$Y = \frac{stress}{longitudinal strain} = \frac{F L}{A Δ L}$
Bulk modulus
$B = - \frac{Δ P}{Δ V / V}$
Compressibility
$K = \frac{1}{B}$
Shear (rigidity) modulus
$η = \frac{shear stress}{shear strain} = \frac{F / A}{θ}$
Poisson's ratio
$σ = - \frac{lateral strain}{longitudinal strain}$
Elastic potential energy
$U = \frac{1}{2} \times stress \times strain \times volume$
Energy density
$u = \frac{1}{2} \frac{stress ^{2}}{Y} = \frac{1}{2} Y (strain)^{2}$
Force constant of a wire
$k = \frac{Y A}{L}$
Extension under load
$Δ L = \frac{F L}{A Y}$
Thermal stress
$stress = Y α Δ T$
Work done in stretching
$W = \frac{1}{2} F Δ L$
Elongation due to own weight
$Δ L = \frac{ρ g L ^{2}}{2 Y}$
Poisson's ratio range
$- 1 \leq σ \leq 0.5$
Volume strain
$\frac{Δ V}{V} = (1 - 2 σ) \frac{Δ L}{L}$
Breaking stress
$stress_{m a x} = \frac{F _{b r e ak}}{A}$
Interatomic force constant
$k = Y r_{0}$
r_0 = interatomic spacing
Torsion of a wire
$τ = \frac{π η r ^{4}}{2 L} θ$
Elastic after-effect
$delay in returning to original state$
Stress–strain: elastic limit
$limit beyond which permanent deformation occurs$

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Elasticity formulas

Elasticity, every formula

Stress

Longitudinal strain

Hooke's law

Young's modulus

Bulk modulus

Compressibility

Shear (rigidity) modulus

Poisson's ratio

Elastic potential energy

Energy density

Force constant of a wire

Extension under load

Thermal stress

Work done in stretching

Elongation due to own weight

Poisson's ratio range

Volume strain

Breaking stress

Interatomic force constant

Torsion of a wire

Elastic after-effect

Stress–strain: elastic limit

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