Calculate the work done, if a wire is loaded by $'Mg'$ weight and the increase in length is $'l'$

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 wire, the elongation in 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 wire is $\frac{1}{2}\, Mg l$

$(IV)$ heat produced is $\frac{1}{2}\, Mg l$ 

Correct statement are :-

Which of the following is true for elastic potential energy density

Two wires of the same material (Young's modulus  $Y$ ) and same length $L$  but radii  $R$  and  $2R$  respectively are joined end to end and a weight  $W$  is suspended from the combination as shown in the figure. The elastic potential energy in the system is

The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{-4}$ is $\dots \; kJ / m ^{3}$. Assume that material is elastic upto the linear strain of $5 \times 10^{-4}$.

A metal wire having Poisson's ratio $1 / 4$ and Young's modulus $8 \times 10^{10} \,N / m ^2$ is stretched by a force, which produces a lateral strain of $0.02 \%$ in it. The elastic potential energy stored per unit volume in wire is [in $\left.J / m ^3\right]$