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

Answer: (C)

$Y=3 \eta(1+\sigma) $
$ Y=3 K(1-\sigma) $
$ \Rightarrow 2 \eta(1+\sigma)=3 K(1-2 \sigma)$
$ \Rightarrow \sigma=\left(\frac{3 K-2 \eta}{6 K+2 \eta}\right)$