Which of the following relations is true for the elastic moduli of a material?

$A$ steel wire of length $2 \ m$ and Young's modulus $2.0 \times 10^{11} \ N/m^2$ is stretched by a force. If Poisson's ratio and transverse strain for the wire are $0.2$ and $10^{-3}$ respectively,then the elastic potential energy density of the wire is . . . . . . $\times 10^5 \ J/m^3$.

$A$ wire is stretched such that its volume remains constant. The Poisson's ratio of the material of the wire is

Give the relation between shear modulus $(G)$ and Young's modulus $(Y)$ for an isotropic material.

For a homogeneous isotropic material, which one of the following cannot be the value of Poisson’s ratio?

When a wire of length $10 \ m$ is subjected to a force of $100 \ N$ along its length, the lateral strain produced is $0.01 \times 10^{-3} \ m$. The Poisson's ratio was found to be $0.4$. If the area of cross-section of the wire is $0.025 \ m^2$, its Young's modulus is: