The strain energy stored in a body of volume $V$ due to shear strain $\phi$ is (shear modulus is $\eta$ )
$\frac{\phi^2 V}{2 \eta}$
$\frac{\phi V^2}{2 \eta}$
$\frac{\phi^2 V}{\eta}$
$\frac{1}{2} \eta \phi^2 V$
A uniform metal rod of $2\,\,mm^2$ cross section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$ . The coefficient of linear expansion of rod is $12\,\,\times\,\,10^{-6}\,/^oC$ . Its Young's modulus of elasticity is $10^{11}\,\,N/m^2$ . The energy stored per unit volume of rod will be ....... $J/m^3$
If $x$ longitudinal strain is produced in a wire of Young's modulus $y,$ then energy stored in the material of the wire per unit volume is
A stretched rubber has
A solid expands upon heating because
What is called elastic energy density ? Write its formula and dimensional formula.