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  4. If Youngs modulus of elasticity Y for a material is one and half times its rigidity coefficient n , the Poisson ratio a will be

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Q. If Youngs modulus of elasticity $Y$ for a material is one and half times its rigidity coefficient $n$ , the Poisson ratio a will be

Haryana PMTHaryana PMT 2009

Solution:

Youngs modulus, $Y=\frac{3 \eta}{2}$
We know that $Y=2 \eta(1+\sigma)$
$\therefore \frac{3 \eta}{2}=2 \eta(1+\sigma)$
$\Rightarrow \sigma=-\frac{1}{4}$