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Pascal's Law

An elastic is...

Question

An elastic isotropic body is subjected to hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio?

A

0.00

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B

0.25

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C

0.50

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D

1.00

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Solution

The correct option is C $0.50$
$Δ V = 0$
$\Rightarrow ϵ_{V} = 0 = \frac{σ}{E} - 2 μ \frac{σ}{E} = \frac{σ}{E} (1 - 2 μ) = 0$
$\Rightarrow= μ = 0.5$

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