Question

A material has Poisson's ratio $0.2$. If a uniform rod of its suffers longitudinal strain $4.0\times {10}^{-3}$, calculate the percentage change in its volume.

• A. $0.15$%
• B. $0.02$%
• C. $0.24$%
• D. $0.48$%

Answer 1

Answer: (C)

$0.24$%

Given:

Poisson's ratio $0.2$.

longitudinal strain $4.0\times {10}^{-3}$

As $\sigma =-\frac{\Delta R/R}{\Delta l/l}$
$\therefore \frac{\Delta R}{R}=-\sigma \frac{\Delta l}{l}=-0.2\times 4.0\times {10}^{-3}=-0.8\times {10}^{-3}$
$V=\pi R^{2}l$
$\therefore \frac{\Delta V}{V}\times 100=(2\frac{\Delta R}{R}+\frac{\Delta l}{l})\times 100=[2\times (-0.8\times {10}^{-3})+4.0\times {10}^{-3}]\times 100=2.4\times {10}^{-3}\times 100=0.24$%