Which of the following relationships is correct for relating the three elastic constants of an isotropic elastic material (where, E = Young's modulus, G = Modulus of rigidity or shear modulus v = Poisson's ratio) ?

ANS:A - E = 2G (1 + v)

The correct relationship for relating the three elastic constants of an isotropic elastic material is: E=2G(1+v) Explanation: In an isotropic elastic material, there are three primary elastic constants: Young's modulus (E), modulus of rigidity or shear modulus (G), and Poisson's ratio (v).

• Young's Modulus (E): It measures the stiffness of the material in the direction of the applied force.
• Modulus of Rigidity or Shear Modulus (G): It measures the material's resistance to shearing forces.
• Poisson's Ratio (v): It describes the lateral strain that occurs when a material is stretched or compressed.

The correct relationship between these elastic constants is given by Hooke's law for isotropic materials, which states that: E=2G(1+v) This equation relates Young's modulus (E) to the shear modulus (G) and Poisson's ratio (v) for isotropic materials. It shows that Young's modulus is related to the shear modulus and Poisson's ratio by a factor of 2(1+v). This relationship holds true for isotropic materials, where mechanical properties are uniform in all directions.