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

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Q. 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.

Mechanical Properties of Solids

Solution:

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