Choose the correct relationship between Poisson ratio , bulk modulus and modulus of rigidity of a given solid object. [2023]

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Solution

Q.
Choose the correct relationship between Poisson ratio $(σ)$ , bulk modulus $(K)$ and modulus of rigidity $(η)$ of a given solid object. [2023]

1 $σ = \frac{3 K - 2 η}{6 K + 2 η}$

2 $σ = \frac{6 K + 2 η}{3 K - 2 η}$

3 $σ = \frac{3 K + 2 η}{6 K + 2 η}$

4 $σ = \frac{6 K - 2 η}{3 K - 2 η}$

Ans.
(1)

$Y = 3 η (1 + σ)$

$Y = 3 K (1 - σ)$

$\Rightarrow 2 η (1 + σ) = 3 K (1 - 2 σ)$

$\Rightarrow σ = (\frac{3 K - 2 η}{6 K + 2 η})$

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Solution

Q. Choose the correct relationship between Poisson ratio (σ), bulk modulus (K) and modulus of rigidity (η) of a given solid object. [2023]

1 σ=3K-2η6K+2η

2 σ=6K+2η3K-2η

3 σ=3K+2η6K+2η

4 σ=6K-2η3K-2η

Ans. (1) Y=3η(1+σ) Y=3K(1-σ) ⇒2η(1+σ)=3K(1-2σ) ⇒σ=(3K-2η6K+2η)

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Q.
Choose the correct relationship between Poisson ratio $(σ)$ , bulk modulus $(K)$ and modulus of rigidity $(η)$ of a given solid object. [2023]

1 $σ = \frac{3 K - 2 η}{6 K + 2 η}$

2 $σ = \frac{6 K + 2 η}{3 K - 2 η}$

3 $σ = \frac{3 K + 2 η}{6 K + 2 η}$

4 $σ = \frac{6 K - 2 η}{3 K - 2 η}$

Ans.
(1)

$Y = 3 η (1 + σ)$

$Y = 3 K (1 - σ)$

$\Rightarrow 2 η (1 + σ) = 3 K (1 - 2 σ)$

$\Rightarrow σ = (\frac{3 K - 2 η}{6 K + 2 η})$