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Q.
A material has Poisson’s ratio $0.50$. If a uniform rod of it suffers a longitudinal strain of $2 × 10^{-3}$, then the percentage change in volume is
Given that the material has a Poisson's ratio is $0.50$ and the longitudinal strain of $2 \times 10^{-3}$. Now the Poisson's ratio is defined as
$v=-\frac{d \varepsilon_{\text {trans }}}{d \varepsilon_{\text {axal }}}=-\frac{d \varepsilon_{y}}{d \varepsilon_{x}}=-\frac{d \varepsilon_{z}}{d \varepsilon_{x}}$
where $v$ is the resulting Poisson's ratio, is transverse strain [negative for axial tension (stretching), positive for axial compression] is axial strain (positive for axial tension, negative for axial compression). Thus there is no change in volume.