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Relationship between Young’s Modulus (E), Shear Modulus (G), and Poisson’s Ratio (μ), for a material obeying the Hooke’s Law, is
1. \(E=\frac{G}{(2~+~\mu)}\)
2. \(E=\frac{2G}{(1~+~\mu)}\)
3. E = G (1 + μ)
4. E = 2G (1 + μ)

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Correct Answer - Option 4 : E = 2G (1 + μ)

Explanation: 

E = Young's Modulus of Rigidity = \(\frac{Stress}{Strain}\)

G = Shear Modulus or Modulus of rigidity = \(\frac{Shear ~stress}{Shear~ strain}\)

μ = Poisson’s ratio = \(-\frac{Lateral~ strain}{Longitudinal~ strain} \)

K = Bulk Modulus of elasticity = \(\frac{Volumetric ~stress}{Volumetric ~strain}\)

Relation between E, K and μ 

  • E = 2G (1 + μ)
  • E = 3K (1 - 2μ)

Combining the two above we get the relation between E, G and K
\(\mathbf{E~=~\frac{9KG}{G~+~3K}}\)

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