Force on individual grain of a grinding wheel is proportional to the square of work speed.

Grinding is a machining process that involves the removal of material from a workpiece using a grinding wheel. The grinding wheel is made up of abrasive grains that are bonded together and rotate at high speeds to perform the cutting action.

Force on individual grain:
When the grinding wheel comes into contact with the workpiece, each individual abrasive grain on the surface of the wheel interacts with the workpiece material. This interaction creates a force on the grain, which is responsible for the material removal.

Factors affecting the force:
The force on an individual grain of the grinding wheel depends on several factors, including the work speed. The work speed refers to the relative speed between the grinding wheel and the workpiece surface.

Explanation:
The force on an individual grain can be understood by considering the cutting action of the grain on the workpiece material. As the grain moves across the workpiece surface, it cuts and removes material. This cutting action requires the application of a cutting force.

The cutting force is influenced by the speed at which the grain moves across the workpiece surface. At higher work speeds, the grain has less time to engage with the workpiece material, resulting in a shorter contact time. This shorter contact time leads to a higher cutting force being applied by the grain.

Mathematically, the force on an individual grain can be expressed as:

F = K * V^n

Where:
F = Force on grain
K = Constant
V = Work speed
n = Exponent

Proportional to the square of work speed:
The relationship between the force on the grain and the work speed can be determined experimentally. It has been observed that the force on the grain is proportional to the square of the work speed (V^2).

This relationship can be explained by considering the cutting action of the grain. The cutting force is directly related to the rate at which material is being removed. At higher work speeds, the rate of material removal increases, leading to a higher cutting force. The square relationship between the force and the work speed can be attributed to the fact that the cutting force is proportional to the product of the work speed and the rate of material removal.

Therefore, the correct answer is option 'B', the force on an individual grain of a grinding wheel is proportional to the square of the work speed.