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

If the Young's modulus of a material is $2.4$ times its modulus of rigidity,what is the Poisson's ratio of the material?

$A$ material has Poisson's ratio $0.5$. If a uniform rod of it suffers a longitudinal strain of $3 \times 10^{-3}$, what will be the percentage increase in volume? .......... $\%$

$A$ wire of length $L$ and radius $r$ is loaded with a weight $Mg$. If $Y$ and $\sigma$ denote the Young's modulus and Poisson's ratio of the material of the wire respectively,then the decrease in the radius of the wire $(\Delta r)$ is given by:

If the Young's modulus for silver is $8 \times 10^{10} \ N/m^2$ and the bulk modulus is $10 \times 10^{10} \ N/m^2$,what is the Poisson's ratio?

$A$ 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