If $x$ longitudinal strain is produced in a wire of Young's modulus $y,$ then energy stored in the material of the wire per unit volume is

$K$ is the force constant of a spring. The work done in increasing its extension from ${l_1}$ to ${l_2}$ will be

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

The length of a rod is $20\, cm$ and area of cross-section $2\,c{m^2}$. The Young's modulus of the material of wire is $1.4 \times {10^{11}}\,N/{m^2}$. If the rod is compressed by $5\, kg-wt$ along its length, then increase in the energy of the rod in joules will be

A $2 \,m$ long rod of radius $1 \,cm$ which is fixed from one end is given a twist of $0.8$ radians. The shear strain developed will be

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 :-