An aluminium rod with Young's modulus $Y = 7.0 \times 10^{10} \ N/m^2$ undergoes elastic strain of $0.04 \%$. The energy per unit volume stored in the rod in $SI$ units is:

The work done in increasing the length of a $1 \ m$ long wire of cross-section area $1 \ mm^2$ by $1 \ mm$ will be ....... $J$ $(Y = 2 \times 10^{11} \ Nm^{-2})$

$A$ 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?

The work to be done to produce a strain of $10^{-3}$ in a steel wire of mass $2.96 \ kg$ and density $7.4 \ g \ cm^{-3}$ is (Young's modulus of steel $= 2 \times 10^{11} \ Nm^{-2}$)

The work done per unit volume to stretch a wire by $1\%$ of its length,having a cross-sectional area of $1\,mm^2$,is: $[Y = 9 \times 10^{11}\,N/m^2]$

If the tension on a wire is removed at once,then