$A$ wire is suspended by one end. At the other end,a weight equivalent to $20 \ N$ force is applied. If the increase in length is $1.0 \ mm$,the increase in energy of the wire will be ....... $J$.

An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

An $8\,m$ long copper wire and $4\,m$ long steel wire,each of cross-section $0.5\,cm^2$,are fastened end to end and stretched by a $500\,N$ force. The elastic potential energy of the system is (Young's modulus: $Y_{cu} = 1 \times 10^{11}\,N/m^2$,$Y_{steel} = 2 \times 10^{11}\,N/m^2$):

$A$ 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 work done per unit volume in stretching a wire is :-

The work done per unit volume to stretch a wire of cross-sectional area $2 \, mm^2$ by $2 \%$ is ....... $MJ/m^3$. Given: Young's modulus $Y = 8 \times 10^{10} \, N/m^2$.