If Y, K and eta are the values of Young's mod | vedclass

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(C) The relationship between Young's modulus $(Y)$,Bulk modulus $(K)$,and modulus of rigidity $(\eta)$ is derived using Poisson's ratio $(\sigma)$.We

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$Y = \frac{9K\eta}{3K + \eta}$

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(C) The relationship between Young's modulus $(Y)$,Bulk modulus $(K)$,and modulus of rigidity $(\eta)$ is derived using Poisson's ratio $(\sigma)$.We know the relations:$Y = 3K(1 - 2\sigma) \implies 1 - 2\sigma = \frac{Y}{3K} \implies 2\sigma = 1 - \frac{Y}{3K} \implies \sigma = \frac{1}{2} - \frac{Y}{6K} \dots (i)$$Y = 2\eta(1 + \sigma) \implies 1 + \sigma = \frac{Y}{2\eta} \implies \sigma = \frac{Y}{2\eta} - 1 \dots (ii)$Equating $(i)$ and $(ii)$:$\frac{1}{2} - \frac{Y}{6K} = \frac{Y}{2\eta} - 1$$1 + \frac{1}{2} = \frac{Y}{2\eta} + \frac{Y}{6K}$$\frac{3}{2} = \frac{3KY + Y\eta}{6K\eta}$$9K\eta = 3KY + Y\eta$$9K\eta = Y(3K + \eta)$$Y = \frac{9K\eta}{3K + \eta}$Thus,the correct relation is $Y = \frac{9K\eta}{3K + \eta}$.

If $Y, K$ and $\eta$ are the values of Young's modulus,bulk modulus,and modulus of rigidity of any material respectively,choose the correct relation for these parameters.

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