The elastic energy stored in a wire of Young's modulus $Y$ is

When a small mass $m$ is suspended at the lower end of an elastic wire having its upper end fixed to a ceiling,there is a loss in gravitational potential energy,let it be $x$,due to the extension of the wire. Mark the correct option.

An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

$A$ 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 the 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 the rod will be ....... $J/m^3$.

Energy stored per unit volume in a stretched wire having Young's modulus $Y$ and stress $S$ is ...........

$A$ rubber band catapult has an initial length of $2 \, cm$ and a cross-sectional area of $5 \, mm^2$. It is stretched by an additional $2 \, cm$ and then released to project a stone of mass $20 \, g$. The velocity of the projected stone is (Young's modulus of rubber $= 5 \times 10^8 \, N/m^2$) (in $ \, m/s$)