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

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(C) The relationship between Young's modulus $(Y)$,modulus of rigidity $(\eta)$,and Poisson's ratio $(\sigma)$ is given by the formula: $Y = 2\eta(1 + \sigma)$.For any metal,the Poisson's ratio $(\sigma)$ lies between $0$ and $0.5$ (typically around $0.3$).Since $(1 + \sigma) > 1$,it follows that $Y = 2\eta(1 + \sigma) > 2\eta$.Therefore,$Y > \eta$ is always true for metals.

Class 11 Physics Mechanical Properties of Solids Poisson's Ratio and relation between Modulus

Medium

Which statement is true for a metal?

A
$Y < \eta$
B
$Y = \eta$
C
$Y > \eta$
D
$Y < 1/\eta$

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Mechanical Properties of Solids

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Poisson's Ratio and relation between Modulus

The minimum and maximum values of Poisson's ratio for a metal lie between

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There is no change in the volume of a wire due to change in its length on stretching. The Poisson's ratio of the material of the wire is

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The relationship between Young's modulus $Y,$ Bulk modulus $K,$ and modulus of rigidity $\eta$ is:

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If the longitudinal strain of a stretched wire is $0.2 \%$ and the Poisson's ratio of the material of the wire is $0.3$,then the volume strain of the wire is (in $\%$)

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For a given material, the Young's modulus is $2.4$ times its modulus of rigidity. Its Poisson's ratio is ......

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Which statement is true for a metal?

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The minimum and maximum values of Poisson's ratio for a metal lie between

There is no change in the volume of a wire due to change in its length on stretching. The Poisson's ratio of the material of the wire is

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