The ratio of shear stress and shear strain of an elastic material, is

First, imagine you have a block of material, like a rubber eraser.

1. What is Shear Stress?
If you push the top surface of the eraser sideways, parallel to the surface, that sideways force spread over the area is called Shear Stress.
It tries to "slide" one part of the material past another, causing internal resistance.

2. What is Shear Strain?
When you push the eraser sideways, it deforms. The top face moves a little compared to the bottom face, and the corners might become slightly slanted. This angular deformation or distortion caused by shear stress is called Shear Strain.

3. The Relationship:
For elastic materials (materials that return to their original shape after the force is removed), there's a constant relationship between the shear stress applied and the shear strain produced.
This constant ratio is a very important property of the material.

The ratio of Shear Stress to Shear Strain is known as:

* Modulus of Rigidity
* Shear Modulus

Both terms, Modulus of Rigidity and Shear Modulus, refer to the exact same property of a material. They tell us how "stiff" a material is against shearing forces. A higher modulus means the material resists shear deformation (sliding/distortion) more effectively.
This property is often denoted by the letter 'G' or 'μ' (mu).

Why other options are incorrect:
* Modulus of Elasticity (or Young's Modulus): This modulus relates normal stress (force pushing or pulling perpendicular to a surface) to normal strain (change in length). It's about stretching or compressing, not shearing.

Therefore, since both Modulus of Rigidity and Shear Modulus describe the ratio of shear stress to shear strain, the correct answer is Both A and B.