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Physics Question on mechanical properties of solids

A material has Poisson?s ratio 0.500.50. If a uniform rod of it suffers a longitudinal strain of 2?10−32 ? 10^{-3}, then the percentage change in volume is

A

0.60.6

B

0.40.4

C

0.20.2

D

zero

Answer

zero

Explanation

Solution

Given that the material has a Poisson's ratio is 0.500.50 and the longitudinal strain of 2×10−32 \times 10^{-3}. Now the Poisson's ratio is defined as
v=−dεtrans dεaxal =−dεydεx=−dεzdεxv=-\frac{d \varepsilon_{\text {trans }}}{d \varepsilon_{\text {axal }}}=-\frac{d \varepsilon_{y}}{d \varepsilon_{x}}=-\frac{d \varepsilon_{z}}{d \varepsilon_{x}}
where vv 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.