What is the work done in stretching a uniform metal wire of length $2 \ m$ to $2.004 \ m$ with an area of cross-section $10^{-6} \ m^2$ (in $J$)? [Young's modulus of the wire = $2 \times 10^{11} \ N/m^2$]

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,$Y = 2.0 \times 10^{11} \, N/m^2$).

The work done in increasing the length of a $1 \, m$ long wire of cross-sectional area $1 \, mm^2$ by $1 \, mm$ is (Given $Y = 2 \times 10^{11} \, N/m^2$): (in $, J$)

$A$ metal wire of length $L$ is suspended vertically from a rigid support. When a body of mass $M$ is attached to the lower end of the wire,the elongation in the wire is $l$. Consider the following statements:
$(I)$ The loss of gravitational potential energy of mass $M$ is $Mgl$.
$(II)$ The elastic potential energy stored in the wire is $Mgl$.
$(III)$ The elastic potential energy stored in the wire is $\frac{1}{2} Mgl$.
$(IV)$ The heat produced is $\frac{1}{2} Mgl$.
Which of the following statements are correct?

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

$A$ suspended long metal wire is stretched a small distance $x$ by a load $W$ in newton suspended at the other end. Select the best answer out of the following.