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:

$A$ wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of stored elastic energy per unit volume in the first and second wire is

Two wires having the same length and material are stretched by the same force. Their diameters are in the ratio $1:3$. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter),when stretched,is (in $:1$)

$A$ rubber pipe of density $1.5 \times 10^3 \, kg/m^3$ and Young's modulus $5 \times 10^6 \, N/m^2$ is suspended from the roof. The length of the pipe is $8 \, m$. What will be the change in length due to its own weight?

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: $Y_{cu} = 1 \times 10^{11}\,N/m^2$,$Y_{steel} = 2 \times 10^{11}\,N/m^2$):

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