(D) The relation between Young's modulus $(Y)$,rigidity modulus $(\eta)$,and Poisson's ratio $(\sigma)$ is given by: $Y = 2\eta(1 + \sigma)$ Dividing

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

(D) The relation between Young's modulus $(Y)$,rigidity modulus $(\eta)$,and Poisson's ratio $(\sigma)$ is given by: $Y = 2\eta(1 + \sigma)$ Dividing both sides by $2\eta$: $\frac{Y}{2\eta} = 1 + \sigma$ $\frac{Y}{2\eta} - 1 = \sigma$ $\sigma = \frac{Y - 2\eta}{2\eta}$ $\sigma = \frac{0.5Y - \eta}{\eta}$ Thus,option $(d)$ is correct.