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 $, J$)

$A$ uniform heavy rod of weight $10 \, N$,cross-sectional area $100 \, \text{cm}^2$ and length $20 \, \text{cm}$ is hanging from a fixed support. The Young's modulus of the material of the rod is $2 \times 10^{11} \, \text{N/m}^2$. Neglecting the lateral contraction,find the elongation of the rod due to its own weight. (In $\times 10^{-10} \, \text{m}$)

$A$ 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$)

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:

When strain is produced in a body within the elastic limit,its internal energy:

Work done in stretching a wire through $1 \ mm$ is $2 \ J$. What amount of work will be done for elongating another wire of same material,with half the length and double the radius of cross-section,by $1 \ mm$ (in $J$)?