Question

When a wire is stretched, its length increases by 0.3% and the diameter decreases by 0.1%. Poisson's ratio of the material of the wire is about

• A. 0.03
• B. 0.333
• C. 0.15
• D. 0.015

Answer 1

The correct option is B 0.333

$\begin{array}{c}\text{Given, increase in length of wire}=0.3\%\\ \text{increase in diameter}=0.1\%\\ \text{We know that,}\\ d=2r\\ \ln \left(d\right)=\ln \left(2\right)+\ln \left(r\right)\\ \text{Differentiating,}\frac{\Delta d}{d}=\frac{\Delta r}{r}\end{array}$

$\begin{array}{cc}& \therefore \Delta r=\frac{-0.1}{100}\left(r\right)=\frac{-r}{1000}(\begin{array}{c}\text{radius is}\\ \text{decreasing})\end{array}\\ & \begin{array}{cc}\Delta l=\frac{0.3}{100}\left(l\right)& =\frac{3l}{1000}\\ \text{Now, poisson's ratio}\left(\sigma \right)& =\frac{\Delta r/r}{\Delta l/l}\\ & =\frac{1/1000}{3/1000}=\frac{1}{3}\\ & =0.333\end{array}\end{array}$