The work to be done to produce a strain of $10^{-3}$ in a steel wire of mass 2.96 kg and density $7.4 \mathrm{~g} \mathrm{~cm}^{-3}$ is

(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )

The Young's modulus and Poisson's ratio of a material are respectively $Y$ and $\sigma$. The force required to decrease the area of cross-section of a wire made of this material by $\triangle A$ is

A metal rod of area of cross-section $3 \mathrm{~cm}^2$ is stretched along its length by applying a force of $9 \times 10^4 \mathrm{~N}$. If the Young's modulus of the material of the rod is $2 \times 10^{11} \mathrm{Nm}^{-2}$, the energy stored per unit volume in the stretched rod is

Two wires $A$ and $B$ made of same material and areas of cross-section in the ratio $1: 2$ are stretched by same force. If the masses of the wires $A$ and $B$ are in the ratio $2: 3$, then the ratio of the elongations of the wires $A$ and $B$ is