Derive the relation between elastic constants.

A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by $1\%$. If the Poisson's ratio for the material of the rod be $0.2$, which of the following statements is correct?

"The volume approximately ...... ."

If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient $\eta ,$ the Poisson's ratio $\sigma$ will be

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

Given the following values for an elastic material: Young's $\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{u}\mathrm{s}=7\times {10}^{10}\mathrm{ }{\mathrm{N}\mathrm{m}}^{-2}$ and $\mathrm{B}\mathrm{u}\mathrm{l}\mathrm{k}\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{u}\mathrm{s}=11\times {10}^{10}\mathrm{ }{\mathrm{N}\mathrm{m}}^{-2}$. The Poisson's ratio of the material is -