$A$ wire of Young's modulus $1.6 \times 10^{12} \,N/m^{2}$ is stretched by a force so as to produce a strain of $2 \times 10^{-4}$. The energy density of the wire is

If one end of a wire is fixed with a rigid support and the other end is stretched by a force of $10 \, N$,then the increase in length is $0.5 \, mm$. The ratio of the energy stored in the wire to the work done in displacing it through $1.5 \, mm$ by the weight is

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:

$A$ rubber band catapult has an initial length of $2 \, cm$ and a cross-sectional area of $5 \, mm^2$. It is stretched by an additional $2 \, cm$ and then released to project a stone of mass $20 \, g$. The velocity of the projected stone is (Young's modulus of rubber $= 5 \times 10^8 \, N/m^2$) (in $ \, m/s$)

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 $, J$)

If $S$ is stress and $Y$ is Young's modulus of the material of a wire,the energy stored in the wire per unit volume is