Two wires A and B are made of same material. Their diameters are in the ratio of $1: 2$ and lengths are in the ratio of $1: 3$. If they are stretched by the same force, then increase in their lengths will be in the ratio of

A thick metal wire of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the wire due to its own weight is ( $Y=$ Young's modulus of the material of the wire)

A stretched wire of a material whose young's modulus $$Y=2 \times 10^{11} ~\mathrm{Nm}^{-2}$$ has poisson's ratio 0.25 . Its lateral strain $$\varepsilon_l=10^{-3}$$. The elastic energy density of the wire is