Question

A wire of mass $M,$ density $\rho$ and radius $R$ is stretched. If $r$ is the change in the radius and $l$ is the change in its length, then Poisson's ratio is given by :

• A. $\frac{\pi l}{\rho Mr{R}^3}$
• B. $\frac{RM\pi }{l\rho r^3}$
• C. $\frac{rM}{\pi l\rho R^3}$
• D. $\frac{lM}{\pi l\rho R^3}$

Answer 1

The correct option is C $\frac{rM}{\pi l\rho R^3}$

Given. mass - M $\mathrm{den}sity-p$ radius - $R$ Change in radius - $\gamma$ Change in length -$l$ $\text{Volume}=\frac{M}{\rho }=\pi R^{2}L$

Poissons Ratio =$\frac{\frac{\Delta d}{d}}{\frac{\Delta l}{l}}$

$\begin{array}{c}=\frac{\frac{2\gamma }{2R}}{\frac{l}{L}}=\frac{\gamma L}{lR}\\ =\frac{\gamma }{lR}\cdot \frac{M}{P\pi R^2}=\frac{M\gamma }{\ell \pi \rho R3}\end{array}$