The work done in increasing the length of a $1 \ m$ long wire of cross-section area $1 \ mm^2$ by $1 \ mm$ will be ....... $J$ $(Y = 2 \times 10^{11} \ Nm^{-2})$

$A$ 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$)

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

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

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

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: