Question

For a homogeneous, isotropic material, the relation between the shear modulus (\( G \)), Young’s modulus (\( E \)), and Poisson’s ratio (\( \nu \)) is \_\_\_\_?

• A. \( G = 2E(1 + \nu) \)
• B. \( 2G = E(1 + \nu) \)
• C. \( E = 2G(1 + \nu) \)
• D. \( 2E = G(1 + \nu) \)

Hint:

In material mechanics, the shear modulus, Young's modulus, and Poisson's ratio are fundamental properties that help describe the material's deformation under various types of stress.

Answer 1

The Correct Option is C

For a homogeneous and isotropic material, the relationship between shear modulus (\( G \)), Young's modulus (\( E \)), and Poisson's ratio (\( \nu \)) is given by the equation: \[ E = 2G(1 + \nu) \] This equation shows that Young’s modulus is related to the shear modulus and Poisson’s ratio, which describes the material’s response to stress and strain.