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

If the work done in stretching a wire by $1 \ mm$ is $2 \ J$,the work necessary for stretching another wire of the same material but with double the radius of cross-section and half the length by $1 \ mm$ is:

$A$ steel uniform rod of length $2L$,cross-sectional area $A$,and mass $M$ is set rotating in a horizontal plane about an axis passing through its center with angular velocity $\omega$. If $Y$ is the Young's modulus for steel,find the total extension in the length of the rod.

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

The work done per unit volume in stretching a wire 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 $Y = 1.1 \times 10^{11} \text{ N/m}^2$)