Question

A material has Poisson’s ratio $0.50$. If a uniform rod of it suffers a longitudinal strain of $2\times 10^{-3}$, then the percentage change in volume is

• A. $0.6$
• B. $0.4$
• C. $0.2$
• D. zero

Answer 1

Answer: (D)

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
$v=-\frac{d{\epsilon }_{\text{trans }}}{d{\epsilon }_{\text{axal }}}=-\frac{d{\epsilon }_y}{d{\epsilon }_x}=-\frac{d{\epsilon }_z}{d{\epsilon }_x}$
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.