Question

Choose the correct relationship between Poisson ratio $(\sigma)$, bulk modulus $( K )$ and modulus of rigidity $(\eta)$ of a given solid object :

• A. $\sigma=\frac{3 K+2 \eta}{6 K+2 \eta}$
• B. $\sigma=\frac{6 K-2 \eta}{3 K-2 \eta}$
• C. $\sigma=\frac{3 K-2 \eta}{6 K+2 \eta}$
• D. $\sigma=\frac{6 K+2 \eta}{3 K-2 \eta}$

Answer 1

The Correct Option is C

The correct answer is (C) : $\sigma=\frac{3 K-2 \eta}{6 K+2 \eta}$
$Y=3\eta (1+\sigma )$
$Y=3K(1-\sigma )$
$\Rightarrow 2\eta (1+\sigma )=3K(1-2\sigma )$
$\Rightarrow \sigma =\left(\frac{3K-2\eta }{6K+2\eta }\right)$