$A$ 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 ........ $J$.

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 $.... \ J$.

The work to be done to produce a strain of $10^{-3}$ in a steel wire of mass $2.96 \ kg$ and density $7.4 \ g \ cm^{-3}$ is (Young's modulus of steel $= 2 \times 10^{11} \ Nm^{-2}$)

One end of a slack wire (Young's modulus $Y$,length $L$ and cross-sectional area $A$) is clamped to a rigid wall and the other end to a block (mass $m$),which rests on a smooth horizontal plane. The block is set in motion with a speed $v$. What is the maximum distance the block will travel after the wire becomes taut?

The elastic potential energy stored in a steel wire of length $20 \, m$ stretched by $2 \, cm$ is $80 \, J$. The cross-sectional area of the wire is $......... \, mm^2$ (Given,$Y = 2.0 \times 10^{11} \, N/m^2$).

If the force constant of a wire is $K$,the work done in increasing the length of the wire by $l$ is