The answer is option 'C': Shear stress and rate of strain.

Newton's law of viscosity, also known as Newtonian fluid behavior, is a fundamental concept in fluid mechanics that describes the relationship between shear stress and rate of strain in a fluid. It was formulated by Sir Isaac Newton in the 17th century and is based on the observation that the deformation of a fluid under the action of an applied force is directly proportional to the shear stress applied to it.

Explanation:

1. Shear stress:
Shear stress (τ) is a measure of the force per unit area that acts parallel to the surface of a fluid as a result of a tangential force applied to it. In other words, it is the force required to cause the fluid to flow or deform. Shear stress is represented mathematically as τ = F/A, where F is the force applied and A is the area over which the force is applied.

2. Rate of strain:
Rate of strain (du/dy) is a measure of the change in velocity of a fluid layer with respect to distance. It represents the deformation or change in shape of the fluid layer due to the applied shear stress. Mathematically, it is given by du/dy = (u2 - u1) / (y2 - y1), where u is the velocity of the fluid layer, and y is the distance perpendicular to the direction of flow.

3. Newton's law of viscosity:
According to Newton's law of viscosity, the shear stress in a fluid is directly proportional to the rate of strain. Mathematically, it can be expressed as τ = μ (du/dy), where μ is the dynamic viscosity of the fluid. The dynamic viscosity is a measure of a fluid's resistance to flow and is influenced by factors such as temperature and pressure.

Conclusion:

In summary, Newton's law of viscosity states that the shear stress in a fluid is directly proportional to the rate of strain. This relationship is fundamental in understanding the behavior of fluids under shear and is widely used in various applications, such as fluid flow analysis, lubrication, and viscosity measurements.