If the volume of a wire remains unchanged when it is stretched,what is the Poisson's ratio for the wire?

If $Y, K$ and $\eta$ are the values of Young's modulus,bulk modulus,and modulus of rigidity of any material respectively,choose the correct relation for these parameters.

There is no change in the volume of a wire due to a change in its length on stretching. The Poisson's ratio of the material of the wire is:

$A$ material has Poisson's ratio $0.50$. If a uniform rod of it suffers a longitudinal strain of $2 \times 10^{-3}$, then the percentage change in volume is

$A$ metal wire having Poisson's ratio $1/4$ and Young's modulus $8 \times 10^{10} \, N/m^2$ is stretched by a force,which produces a lateral strain of $0.02 \%$ in it. The elastic potential energy stored per unit volume in the wire is [in $J/m^3$]

On all the six surfaces of a unit cube,an equal tensile force of $F$ is applied. The increase in length of each side will be ($Y =$ Young's modulus,$\sigma =$ Poisson's ratio).