Frictional force is the force that opposes the relative motion of two surfaces in contact. It is a fundamental force that plays a crucial role in everyday life, from walking on the ground to driving a car. The dimensional formula of frictional force can be derived using the principle of dimensional analysis.

Derivation of Dimensional Formula of Frictional Force

The frictional force depends on several factors, such as the normal force, the coefficient of friction, and the area of contact. Using the principle of dimensional analysis, we can express the frictional force in terms of these factors.

The formula for frictional force is given by
Frictional force = Coefficient of friction x Normal force

The dimensional formula of frictional force can be derived as follows:

Frictional force = [M^1L^1T^-2]
Coefficient of friction = [Dimensionless]
Normal force = [M^1L^1T^-2]

Substituting the dimensions of coefficient of friction and normal force in the formula for frictional force, we get:

[M^1L^1T^-2] = [Dimensionless] x [M^1L^1T^-2]

Simplifying the above equation, we get:

[M^1L^1T^-2] = [M^1L^1T^-2]

Therefore, the dimensional formula of frictional force is [M^1L^1T^-2].

Explanation of the Dimensional Formula

The dimensional formula of frictional force indicates that it has units of force, which are expressed as N or kg m/s^2. This means that the frictional force is directly proportional to the product of the mass and acceleration. The dimension of length indicates that the frictional force is a vector quantity that has both magnitude and direction. The dimension of time indicates that the frictional force is a dynamic force that changes with time.

In conclusion, the dimensional formula of frictional force is [M^1L^1T^-2]. It represents the units of force, mass, length, and time that are involved in the frictional force. Understanding the dimensional formula of frictional force is important in physics, as it helps us to analyze and derive equations for various physical phenomena involving friction.

the dimensional formula of force is M^1L^1T^-2this is common for all types of forces....true for frictional force too.