The work done on a wire of volume $2 \,cm^3$ is $16 \times 10^2 \,J$. If the Young's modulus of the material of the wire is $4 \times 10^{12} \,N/m^2$, then the strain produced in the wire is:

Energy stored per unit volume in a stretched wire having Young's modulus $Y$ and stress $S$ is ...........

If $S$ is stress and $Y$ is Young's modulus of the material of a wire,the energy stored in the wire per unit volume is

Work done by the restoring force in a string within the elastic limit is $-10 \, J$. The maximum amount of heat produced in the string is .......... $J$.

$A$ 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?

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