$A$ wire $2 \,m$ in length suspended vertically stretches by $10 \,mm$ when a mass of $10 \,kg$ is attached to the lower end. The elastic potential energy gained by the wire is ...... $J$ (take $g=10 \,m/s^2$)

$A$ 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

An $8\,m$ long copper wire and $4\,m$ long steel wire,each of cross-section $0.5\,cm^2$,are fastened end to end and stretched by a $500\,N$ force. The elastic potential energy of the system is (Young's modulus: $Y_{cu} = 1 \times 10^{11}\,N/m^2$,$Y_{steel} = 2 \times 10^{11}\,N/m^2$):

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:

Wires $A$ and $B$ are made from the same material. $A$ has twice the diameter and three times the length of $B$. If the elastic limits are not reached,when each is stretched by the same tension,the ratio of energy stored in $A$ to that in $B$ 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$)