Question

A material has Poisson's ratio $0.3$.If a uniform rod of its suffers a longitudinal strain of $3\times {10}^{-3}$, what will be the percentage increase in volume?

Answer 1

Poisson's ratio$=\sigma =\frac{-\Delta R/R}{\Delta L/L}$

$⟹\frac{\Delta R}{R}=-0.3\frac{\Delta L}{L}$

$V=\pi R^{2}L$

$⟹\frac{\Delta V}{V}=2\frac{\Delta R}{R}+\frac{\Delta L}{L}$

$⟹\frac{\Delta V}{V}=0.4\frac{\Delta L}{L}=0.4\times 3\times {10}^{-3}$

Hence, $\frac{\Delta V}{V}\times 100=0.12\%$