When a force is applied on a wire of uniform cross-sectional area $3 \times 10^{-6} \, m^2$ and length $4 \, m$,the increase in length is $1 \, mm$. The energy stored in it will be $(Y = 2 \times 10^{11} \, N/m^2)$. (in $, J$)

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:

$A$ rubber pipe of density $1.5 \times 10^3 \, kg/m^3$ and Young's modulus $5 \times 10^6 \, N/m^2$ is suspended from the roof. The length of the pipe is $8 \, m$. What will be the change in length due to its own weight?

The force constant of a wire is $k$ and that of another wire is $2k$. When both the wires are stretched through the same distance,then the work done is:

$A$ uniform metal rod of $2\, mm^2$ cross-section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$. The coefficient of linear expansion of the rod is $12 \times 10^{-6}/^oC$. Its Young's modulus of elasticity is $10^{11} \,N/m^2$. The energy stored per unit volume of the rod will be ....... $J/m^3$.

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 .......... $J$.