Question

A material has Poisson's ratio $0.5$. If a uniform rod of it suffers a longitudinal strain of $3\times {10}^{-3}$, what will be percentage increase in volume?

• A. $2\%$
• B. $3\%$
• C. $5\%$
• D. $0\%$

Answer 1

Answer: (D)

$0\%$

$\begin{array}{c}\mu \text{, poisson's ratio}=0.5\\ \frac{\Delta l}{l}=3\times {10}^{-3}\\ \text{To find:}\frac{\Delta V}{V}\times 100=\text{percentage increase in volume.}\\ \mu =\frac{1}{2}-\frac{Y}{6B}\end{array}$

$\begin{array}{c}\Rightarrow \frac{1}{2}=\frac{1}{2}-\frac{Y}{6B}\\ \Rightarrow \frac{Y}{6B}=0\\ B\to \infty \\ \left|\frac{F}{A}\right|=|B-\frac{\Delta V}{V}|\\ \Rightarrow \left|\frac{\Delta V}{V}\right|=\left|\frac{F}{BA}\right|\\ asB⟶\infty \\ \frac{\Delta V}{V}⟶0.\end{array}$

$\begin{array}{c}\text{Hence :}\frac{\Delta V}{V}\times 100=0\%\\ \text{Ans :}D\end{array}$