Question

In terms of bulk modulus (K) and modulus of rigidity (G), Poisson's ratio can be expressed as

• A. $\frac{3K-4G}{6K+4G}$
• B. $\frac{3K+4G}{6K-4G}$
• C. $\frac{3K-2G}{6K+2G}$
• D. $\frac{3K+2G}{6K-2G}$

Answer 1

The correct option is C $\frac{3K-2G}{6K+2G}$

There are four elastic constants viz.
E = Young's modulus of elasticity
G = Modulus of rigidity
K = Bulk modulus
μ = Poisson's ratio
The relations between these constants are:
(i) $G=\frac{E}{2(1+\mu )}$

(ii) $K=\frac{E}{3(1-2\mu )}$

(iii) $E=\frac{9KG}{G+3K}$

(iv) $\mu =\frac{3K-2G}{6K+2G}$