The work done per unit volume to stretch a wire of cross-sectional area $2 \, mm^2$ by $2 \%$ is ....... $MJ/m^3$. Given: Young's modulus $Y = 8 \times 10^{10} \, N/m^2$.

$A$ steel rod of length $\ell$,cross-sectional area $A$,Young's modulus of elasticity $Y$,and thermal coefficient of linear expansion $\alpha$ is heated so that its temperature increases by $t\,^\circ C$. The work that can be done by the rod on heating is:

Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires,when stretched by the same force,will be in the ratio: (in $:1$)

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

The force constant of a wire is $k$ and that of another wire is $2k$. When both the wires are stretched through the same distance,then the work done is:

If the tension on a wire is removed at once,then