Question

A material has Poissons ratio $0.5$. If a uniform rod made of the surface a longitudinal string of $2\times {10}^{-3}$, what is the percentage increase in its volume?

• A. $2\%$
• B. $4\%$
• C. $0\%$
• D. $5\%$

Answer 1

The correct option is C $0\%$

Given, Poissons ratio $=0.5$

$\begin{array}{c}\text{longitudinal strain}=2\times {10}^{-3}\\ \begin{array}{cc}\frac{\Delta l}{l}& =2\times {10}^{-3}\\ \sigma & =-\frac{\Delta r/r}{\Delta x/l}\\ \frac{\Delta r}{\gamma }& =\frac{-1}{\text{/}}\times \text{/}2\times {10}^{-3}=-{10}^{-3}\end{array}\end{array}$For red, $V=\pi r^{2}d$

$\ln v=\ln \pi +2\ln r+\ln \left(l\right)$

Differentiating

$\begin{array}{cc}\frac{\Delta V}{V}& =\frac{2\Delta r}{\gamma }+\frac{\Delta l}{l}\\ & =-2\times {10}^{-3}+2\times {10}^{-3}\\ \frac{\Delta V}{V}& =0\end{array}$

$\therefore$ There is no change in the volume.