Question

Poisson`s ratio of a material is $0.5$ applied to wire of this material, these in the cross-section area increase in the length is.

Answer 1

Given Poisson's ratio$ (⊂) = 0.5.$

Here, density is constant and hence change in volume is $0$.

Given that there is a decrease in cross-sectional area by $4$

So, $\left(\frac{dA}{A}\right)=4.$

We know that $dA/A=2\ast \left(dr/r\right).$

$4=2\times \left(\frac{dr}{r}\right)$

$2=\left(\frac{dr}{r}\right).$

Hence,

$=\frac{dl}{l}$

$= (\dfrac{dr}{r})/⊂$

$=\frac{2}{0.5}$

$=4.$

Therefore, the % increase in length $=4$