The correct relationship between Modulus of Elasticity (E) and Shear Modulus (G) is given by:

Explanation:

The relationship between the Modulus of Elasticity (E) and the Shear Modulus (G) for an isotropic material is given by the formula:

E=2G(1+μ)

Additional InformationModulus of Elasticity (E):

1. Definition: The Modulus of Elasticity (E), also known as Young's Modulus, is a material property that measures the stiffness of a material in response to uniaxial tensile or compressive stress. It is defined as the ratio of stress to strain in the elastic region of the material’s stress-strain curve.

2. Significance: A higher E value means the material is stiffer and deforms less under stress. It is an important factor in structural design and material selection.

3. Example: Steel has a higher E value than rubber, meaning steel is much stiffer and less deformable than rubber under the same load.

Shear Modulus (G):

1. Definition: The Shear Modulus (G), also known as Modulus of Rigidity, measures the material's response to shear stress (forces that cause deformation by sliding layers of material). It is defined as the ratio of shear stress to shear strain in the elastic region of the material’s behavior.

2. Significance: G indicates how easily a material deforms under shear forces. Materials with a high G are resistant to shape changes when subjected to shear forces.

3. Example: Steel has a higher G than rubber, meaning steel resists deformation under shear forces more effectively than rubber.