The work done in increasing the length of a $1 \ m$ long wire of cross-section area $1 \ mm^2$ by $1 \ mm$ will be ....... $J$ $(Y = 2 \times 10^{11} \ Nm^{-2})$

$A$ wire suspended vertically from one of its ends is stretched by attaching a weight of $200\, N$ to the lower end. The weight stretches the wire by $1\, mm$. Then the elastic energy stored in the wire is ........ $J$.

The energy stored in a strained wire is given by

$A$ wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of stored elastic energy per unit volume in the first and second wire is

The work done per unit volume in stretching a wire is :-

The length of a rod is $20 \, cm$ and the area of cross-section is $2 \, cm^2$. The Young's modulus of the material of the rod is $1.4 \times 10^{11} \, N/m^2$. If the rod is compressed by a force of $5 \, kg-wt$ along its length,then the increase in the elastic potential energy of the rod in joules will be: