For an elastic material,what is the relations | vedclass

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

Vedclass · Accepted Answer

$Y > \eta$

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(D) The relationship between Young's modulus $(Y)$ and the modulus of rigidity (shear modulus,$\eta$) is given by the formula:$Y = 2\eta(1 + \sigma)$where $\sigma$ is the Poisson's ratio.The practical range for Poisson's ratio $(\sigma)$ for most materials is $0 Substituting the minimum value of $\sigma$ (which is $0$):$Y = 2\eta(1 + 0) = 2\eta$Substituting the maximum value of $\sigma$ (which is $0.5$):$Y = 2\eta(1 + 0.5) = 2\eta(1.5) = 3\eta$Since $Y$ ranges from $2\eta$ to $3\eta$ for valid materials,it is clear that $Y > \eta$ always holds true for elastic materials.

For an elastic material,what is the relationship between Young's modulus $(Y)$ and the modulus of rigidity $(\eta)$?

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