Principle of Homogeneity of Dimensions - QS Study
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An equation is dimensionally correct if the dimensions of the various terms on either side of the equation are the same. This is called the principle of homogeneity of dimensions. This principle is based on the fact that two quantities of the same dimension only can be added up, the resulting quantity also possessing the same dimension.

The equation A + B = C is valid only if the dimensions of A. B and C are the same.

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Uses of dimensional analysis: The method of dimensional analysis is used to

(i) convert a physical quantity from one system of units to another.

(ii) check the dimensional correctness of a given equation.

(iii) establish a relationship between different physical quantities in an equation.