Question

A material has Poisson’s ratio $0.30$. If a uniform rod suffers a longitudinal strain of $3\times 10^{-4}$, then the percentage change in volume.

• A. $0.05\%$
• B. $0.02\%$
• C. $0.01\%$
• D. $0.08\%$

Answer 1

Answer: (C)

$\frac{\Delta V}{V}=(1-2\sigma )\frac{\Delta L}{L}$
$\Rightarrow \frac{\Delta V}{V}=(1-2\times 0.30)3\times 10^{-4}$
$\therefore \frac{\Delta V}{V}=0.4\times 3\times 10^{-4}=1.2\times 10^{-4}$
$\Rightarrow \frac{\Delta V}{V}=0.01\times 10^{-2}$
$\therefore \frac{\Delta V}{V}\times 100=1.2\times 10^{-4}\times 100=0.012\%$