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 $Y = 8 \times 10^{10} \, N/m^2$.

Which of the following is true for elastic potential energy density?

$A$ 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 ....... $J/m^3$.

$A$ suspended long metal wire is stretched a small distance $x$ by a load $W$ in newton suspended at the other end. Select the best answer out of the following.

$A$ stone of mass $20 \, g$ is projected from a rubber catapult of length $0.1 \, m$ and area of cross-section $10^{-6} \, m^2$,stretched by an amount $0.04 \, m$. The velocity of the projected stone is $.... \, m/s$. (Young's modulus of rubber $= 0.5 \times 10^9 \, N/m^2$)

Two wires of the same diameter and the same material have lengths $l$ and $2l$. If the same force $F$ is applied to each,what is the ratio of the work done in stretching the two wires?