The elastic moduli are related to each other and Poisson's ratio ($\nu$) by several equations. The standard relations are $E = 3K(1 - 2\nu)$ and $E = 2N(1 + \nu)$. Eliminating Poisson's ratio from these two equations leads to the combined relation: $E = \frac{9KN}{3K+N}$, which can be rearranged to $\frac{1}{E} = \frac{3K+N}{9KN} = \frac{3K}{9KN} + \frac{N}{9KN} = \frac{1}{3N} + \frac{1}{9K}$. Multiplying by 9 gives $9/E = 3/ N + 1/K$.
The relation connecting Young's modulus (E), Bulk modulus (K) and Rigidity modulus (N) is
Asked in TNPSC CS Prelims 2015 · Topic: Physical Properties of Materials (Elasticity and Plasticity)
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Answer: A. $\frac{9}{E} = \frac{3}{N} + \frac{1}{K}$
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