Discussion
In terms of bulk modulus (K) and modulus of rigidity (G), the Poisson's ratio can be expressed as:
Answer: C
Poisson's ratio is (3K - 2G) / (6K + 2G).
Start from the two standard relations between the elastic constants:
\[ \begin{aligned} E &= 3K(1 - 2\mu) \\ E &= 2G(1 + \mu) \end{aligned} \]
Equating them and solving for \(\mu\):
\[ \begin{aligned} 3K - 6K\mu &= 2G + 2G\mu \\ \mu &= \frac{3K - 2G}{6K + 2G} \end{aligned} \]
Check: the formula gives \(\mu = 0.5\) only when K is infinitely large compared with G, that is, for an incompressible material. The options with 4G do not follow from the two relations.
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