When a shear stress is applied to a substance and it resists it by static deformation, the substance is classified as a solid.

Shear stress is a type of stress that occurs when two layers of a substance slide against each other in opposite directions. It is represented as the force per unit area parallel to the plane of the layers. When shear stress is applied to a substance, it causes the substance to undergo deformation or distortion.

Here are the reasons why the correct answer is option 'B' (Solid):

1. Definition of a solid: A solid is a state of matter characterized by a definite shape and volume. Solids have strong intermolecular forces and resist deformation under the influence of external forces.

2. Static deformation: When a solid is subjected to shear stress, it undergoes static deformation. Static deformation refers to the change in shape or size of a material without any change in its volume. The solid deforms under the applied shear stress but remains in its deformed state when the stress is removed.

3. Resistance to shear stress: Solids have a high resistance to shear stress due to the strong intermolecular forces between their particles. These forces hold the particles in a fixed position, allowing the solid to maintain its shape and resist deformation.

4. Lack of fluidity: Unlike liquids and gases, solids do not flow and cannot be easily compressed. This lack of fluidity is a characteristic of solids and contributes to their ability to resist shear stress.

5. Structural integrity: Solids have a well-defined and ordered arrangement of particles, which gives them a stable and rigid structure. This structural integrity enables solids to withstand shear stress without significant deformation.

In conclusion, when a substance resists shear stress through static deformation, it is classified as a solid. Solids have a definite shape and volume, lack fluidity, and possess strong intermolecular forces that allow them to maintain their shape and resist deformation.