The elastic potential energy stored in a steel wire of length $20 \, m$ stretched by $2 \, cm$ is $80 \, J$. The cross-sectional area of the wire is $......... \, mm^2$ (Given,$Y = 2.0 \times 10^{11} \, N/m^2$).

$A$ rubber cord catapult has a cross-sectional area of $25\,mm^2$ and an initial length of $10\,cm$. It is stretched by $5\,cm$ and then released to project a missile of mass $5\,g$. Taking $Y_{rubber} = 5 \times 10^8\,N/m^2$,the velocity of the projected missile is ......... $m/s$.

Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires,when stretched by the same force,will be in the ratio: (in $:1$)

Calculate the work done, if a wire is loaded by $Mg$ weight and the increase in length is $l$.

$A$ 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 $= 0.5 \times 10^9 \, N/m^2$)

$A$ wire of length $25 \ cm$ and radius $2 \ mm$ is fixed at one end. If a torque is applied at the other end to produce an angular displacement of $45^o$,calculate the work done in $J$. (Given: $\eta = 8 \times 10^{10} \ N/m^2$)