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

Question

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

Tardigrade Admin · Accepted Answer

Y=3 η(1+σ) Y=3 K(1-σ) ⇒ 2 η(1+σ)=3 K(1-2 σ) ⇒ σ=((3 K-2 η/6 K+2 η))

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

$σ = \frac{3 K + 2 η}{6 K + 2 η}$

$σ = \frac{6 K - 2 η}{3 K - 2 η}$

$σ = \frac{3 K - 2 η}{6 K + 2 η}$

$σ = \frac{6 K + 2 η}{3 K - 2 η}$

$Y = 3 η (1 + σ)$
$Y = 3 K (1 - σ)$
$\Rightarrow 2 η (1 + σ) = 3 K (1 - 2 σ)$
$\Rightarrow σ = (\frac{3 K - 2 η}{6 K + 2 η})$

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

σ=6K+2η3K+2η​

σ=3K−2η6K−2η​

σ=6K+2η3K−2η​

σ=3K−2η6K+2η​