If the work done in stretching a wire by $1 \ mm$ is $2 \ J$,the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by $1 \ mm$ is $.... \ J$.

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.

The energy stored in a strained wire is given by

$A$ metal rod of area of cross-section $3 \,cm^2$ is stretched along its length by applying a force of $9 \times 10^4 \,N$. If the Young's modulus of the material of the rod is $2 \times 10^{11} \,Nm^{-2}$, the energy stored per unit volume in the stretched rod is:

$A$ wire of Young's modulus $1.6 \times 10^{12} \,N/m^{2}$ is stretched by a force so as to produce a strain of $2 \times 10^{-4}$. The energy density of the wire is

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