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Question

(A) The relationships between Young's modulus $(Y)$,bulk modulus $(K)$,modulus of rigidity $(\eta)$,and Poisson's ratio $(\sigma)$ are given by:$Y = 2

Vedclass · Accepted Answer

$\sigma=\frac{3 K -2 \eta}{6 K +2 \eta}$

Vedclass · Answer

(A) The relationships between Young's modulus $(Y)$,bulk modulus $(K)$,modulus of rigidity $(\eta)$,and Poisson's ratio $(\sigma)$ are given by:$Y = 2\eta(1+\sigma)$  --- $(1)$$Y = 3K(1-2\sigma)$  --- $(2)$Equating the two expressions for $Y$:$2\eta(1+\sigma) = 3K(1-2\sigma)$$2\eta + 2\eta\sigma = 3K - 6K\sigma$$2\eta\sigma + 6K\sigma = 3K - 2\eta$$\sigma(6K + 2\eta) = 3K - 2\eta$$\sigma = \frac{3K - 2\eta}{6K + 2\eta}$

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

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