Question

A uniform rod undergoes a longitudinal strain of $2$. find percentage change in its volume if poisson's ratio of the material is $0.50$

• A. 0.4%
• B. 0.7%
• C. 0%
• D. 0.3%

Answer 1

The correct option is C 0%

We know that realtion between moduler of elasticity $\left(\epsilon \right),$ possion's ratio $\left(u\right)$ and balls modules elasticity $\left(h\right).$

Given by,

$\Rightarrow \epsilon =3h(1-2u)$

here given $u=0.3$

$h\to \alpha$

and we also know $\to h=\frac{\frac{-△p}{△v}}{v}$

If $h$ tends to infinite then $△v$ tends to zero.

$\%$ change in volume will be zero.

Hence, solve.