Choose the correct relationship between Poisson ratio (σ), bulk modulus (K) and modulus of rigidity (η) of a given solid object: (a) σ = (3K+2η)/(6K+2η) (b) σ = (3K-2η)/(6K+2η) (c) σ = (6K+2η)/(3K-2η) (d) σ = (6K-2η)/(3K-2η)

Answer: (b). Y = 3K(1-2σ) and Y = 2η(1+σ) Equate: 3K - 6Kσ = 2η + 2ησ σ(6K + 2η) = 3K - 2η ⇒ σ = (3K-2η)/(6K+2η) So the answer is (b).

Choose the correct relationship between Poisson ratio (σ), bulk… | JEE Main 2023 (30 Jan, Shift 1)

Q5JEE Main 2023 · 30 JAN · SHIFT 1Easy

Shear Modulus & Poisson's Ratio

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

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Answer: (b)

$Y = 3K(1-2\sigma)$ and $Y = 2\eta(1+\sigma)$
Equate: $3K - 6K\sigma = 2\eta + 2\eta\sigma$
$\sigma(6K + 2\eta) = 3K - 2\eta \Rightarrow \sigma = \frac{3K-2\eta}{6K+2\eta}$
So the answer is (b).

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