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(C) For isotropic materials, the elastic moduli are related by Poisson's ratio $\sigma$ as follows:$Y = 2n(1 + \sigma)$$Y = 3k(1 - 2\sigma)$Where $Y$

Vedclass · Accepted Answer

Shear modulus < Young's modulus < bulk modulus

Vedclass · Answer

(C) For isotropic materials, the elastic moduli are related by Poisson's ratio $\sigma$ as follows:$Y = 2n(1 + \sigma)$$Y = 3k(1 - 2\sigma)$Where $Y$ is Young's modulus, $n$ is shear modulus (rigidity), and $k$ is bulk modulus.For most metals like aluminium and copper, the Poisson's ratio $\sigma$ lies between $0$ and $0.5$ (typically around $0.3$).Since $0 From $Y = 2n(1 + \sigma)$, since $(1 + \sigma) > 1$, we get $Y > n$.From $Y = 3k(1 - 2\sigma)$, since $(1 - 2\sigma) Y/3$.Comparing the magnitudes for typical metals, the relationship is $n Therefore, the correct order is shear modulus < Young's modulus < bulk modulus.

In materials like aluminium and copper, the correct order of magnitude of various elastic moduli is:

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