The elastic potential energy stored in a steel wire of length $20 \, m$ stretched by $2 \, cm$ is $80 \, J$. The cross-sectional area of the wire is $......... \, mm^2$ (Given, $Y = 2.0 \times 10^{11} \, N/m^2$).

$A$ uniform rod of length $L$ has a mass per unit length $\lambda$ and area of cross-section $A$. If the Young's modulus of the rod is $Y$,then the elongation in the rod due to its own weight is:

The work done in increasing the length of a $1 \, m$ long wire of cross-sectional area $1 \, mm^2$ by $1 \, mm$ is (Given $Y = 2 \times 10^{11} \, N/m^2$): (in $, J$)

$A$ wire of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y$. It is stretched by an amount $x$. The work done is

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

$A$ copper wire of length $3 \text{ m}$ is stretched by $3 \text{ mm}$ by applying an external force. The volume of the wire is $600 \times 10^{-6} \text{ m}^3$. The elastic potential energy stored in the wire in the stretched condition is . . . . . . $\text{J}$. (Given Young's modulus of copper $Y = 1.1 \times 10^{11} \text{ N/m}^2$)