Question

A material has Poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of $2\times {10}^{-3}$, then the percentage increase in its volume is

• A. 0%
• B. 10%
• C. 20%
• D. 5%

Answer 1

Answer: (A)

0%

$\begin{array}{c}\left(\mu \right)\text{Poisson's ratio can be related to young's modulus}\\ \text{and Bulk modulus as follows}\\ \mu =\frac{1}{2}-\frac{Y}{6B}\\ \Rightarrow \frac{1}{2}=\frac{1}{2}\frac{Y}{2B}....(\mu =\frac{1}{2}\to \text{given})\end{array}$

$\begin{array}{c}\Rightarrow \frac{Y}{2B}=0\\ B⟶\infty \end{array}$

$B=\frac{\Delta P}{\Delta V/V}\text{will tend to infinily if}\Delta V\approx 0$

$\begin{array}{c}\text{Hence}\frac{\Delta V}{V}\times 100=0\%\\ \text{Hence , percentage increase in its volume is}0\%\\ \text{Ans:}⟶A\text{.}\end{array}$