Mechanical Properties of Solids

JEE Main level, single correct, medium

94 of 118

Question 94 of 118

Choose the correct relationship between Poisson ratio (σ)\left(\sigma \right), bulk modulus (K)(K) and modulus of rigidity (η)\left(\eta \right) of a given solid object:

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Answer: (A) σ=3K−2η6K+2η\sigma =\dfrac{3K-2\eta }{6K+2\eta }

The relations of Young's modulus, YY, bulk modulus, KK, the modulus of rigidity, η\eta and Poisson's ratio, σ\sigma are given as
Y=3K(1−2σ)…(1)Y=3K(1-2\sigma )\ldots \left(1\right) and
Y=2η(1+σ)…(2)Y=2\eta \left(1+\sigma \right)\ldots \left(2\right)
From equation (1)and(2)\left(1\right)and\left(2\right), we have
⇒2η(1+σ)=3K(1−2σ)\Rightarrow 2\eta \left(1+\sigma \right)=3K\left(1-2\sigma \right)
⇒σ=(3K−2η6K+2η)\Rightarrow \sigma =\left(\dfrac{3K-2\eta }{6K+2\eta }\right)

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