$A$ 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.

$A$ 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?

Two wires having the same length and material are stretched by the same force. Their diameters are in the ratio $1:3$. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter),when stretched,is (in $:1$)

The length of a wire is $1.0 \, m$ and the area of cross-section is $1.0 \times 10^{-2} \, cm^2$. If the work done for an increase in length by $0.2 \, cm$ is $0.4 \, J$,then the Young's modulus of the material of the wire is:

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

$A$ wire fixed at the upper end stretches by length $l$ by applying a force $F$. The work done in stretching is