The elastic potential energy stored in a copper rod of length one metre and area of cross-section $1 \mathrm{~mm}^2$ when stretched by 1 mm is

(Young's modulus of copper $=1.2 \times 10^{11} \mathrm{Nm}^{-2}$ )

A wire of length 0.5 m and area of cross-section $4 \times 10^{-6} \mathrm{~m}^2$ at a temperature of $100^{\circ} \mathrm{C}$ is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to $0^{\circ} \mathrm{C}$, but is prevented from contracting by attaching a mass at the lower end. If the mass of the wire is negligible, then the value of the mass attached to the wire is

[Young's modulus of material of the wire $=10^{11} \mathrm{Nm}^{-2}$, coefficient of linear expansion of the material of the wire $=10^{-5} \mathrm{~K}^{-1}$ and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ ]

A wire is stretched 1 mm by a force $F$. If a second wire of same material, same length and 4 times the diameter of the first wire is stretched by the same force $F$, then the elongation of the second wire is

If the longitudinal strain of a stretched wire is $0.2 \%$ and the Poisson's ratio of the material of the wire is 0.3 , then the volume strain of the wire is