Which of the following relations is true?

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(D) The relationship between Young's modulus $(Y)$,Bulk modulus $(K)$,and Modulus of rigidity $(\eta)$ is given by the formula: $Y = 2\eta(1 + \sigma)

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$\sigma = \frac{0.5Y - \eta}{\eta}$

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(D) The relationship between Young's modulus $(Y)$,Bulk modulus $(K)$,and Modulus of rigidity $(\eta)$ is given by the formula: $Y = 2\eta(1 + \sigma)$.Rearranging this equation to solve for Poisson's ratio $(\sigma)$:$Y = 2\eta + 2\eta\sigma$$Y - 2\eta = 2\eta\sigma$$\sigma = \frac{Y - 2\eta}{2\eta}$$\sigma = \frac{Y}{2\eta} - \frac{2\eta}{2\eta}$$\sigma = \frac{0.5Y}{\eta} - 1$Alternatively,expressing it as $\sigma = \frac{0.5Y - \eta}{\eta}$ matches option $D$.

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