What is homogeneity principle??

Principle of Homogeneity of Dimensions

The principle of homogeneity of dimensions states that “For an equation to be dimensionally correct, the dimensions of each term on “Left Hand Side” must be equivalent to the dimensions of each term on “Right Hand Side.” So, it states that if the dimensions of each term on both the sides of the equation are similar, then the physical measurement will be accurate.

Dimensional formula of final velocity, v = [LT-1]

Dimensional formula of final velocity, u = [LT-1]

Dimensional formula of acceleration x time, at = [LT-2 × T] = [LT-1]

Following are the main uses of dimensional analysis –

The method of dimensional analysis is used to:

(a) Checking the dimensional correctness of a physical equation. If the dimensions follow the principle of homogeneity, the equation is dimensionally approved, otherwise not.

(b) Deriving the relationship between different physical quantities; in many cases, we can find the expression for a physical quantity, if we know the factors on which it depends.

(c) Conversion of one system of units into another. This fact helps us to change one system of units into another.

(d) Convert a physical quantity from one system of units to another.

(e) Check the dimensional correctness of a given equation.

(f) Establish a relationship between different physical quantities in an equation.