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 :-

The Young's modulus of a wire is $Y.$ If the energy per unit volume is $E$, then the strain will be

A uniform metal rod of $2\, mm^2$ cross section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$. The coefficient of linear expansion of rod is $12\times10^{-6}/^oC$. Its Young's modulus of elasticity is $10^{11} \,N/m^2$. The energy stored per unit volume of rod will be ....... $J/m^3$

The work done in stretching an elastic wire per unit volume is 

When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by $2\, cms$. The work required to be done by an external agent in stretching this spring by $5\, cms$ will be ......... $joule$       $(g = 9.8\,metres/se{c^2})$

An Indian rubber cord $L$ metre long and area of cross-section $A$ $metr{e^2}$ is suspended vertically. Density of rubber is $D$ $kg/metr{e^3}$ and Young's modulus of rubber is $E$ $newton/metr{e^2}$. If the wire extends by $l$ metre under its own weight, then extension $l$ is