The increase in length on stretching a wire is $0.05\%$. If its Poisson's ratio is $0.4$,then its diameter

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).

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

$A$ copper wire of cross-sectional area $0.01 \,cm^2$ is under a tension of $22 \,N$. The decrease in the cross-sectional area is (Young modulus $= 1.1 \times 10^{11} \,N/m^2$, Poisson's ratio $= 0.32$)

$A$ 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 $J/m^3$]

$A 3 \ m$ long steel wire is stretched to increase its length by $0.3 \ cm$. Poisson's ratio for steel is $0.26$. The lateral strain produced in the wire is