We say formulas used in physics are consistent with SI unit. The quantities that are independent of other quantities are called fundamental quantities. The units that are used to measure these fundamental quantities are called fundamental units. Dimensions of a physical quantity are the powers to which the fundamental units are raised to obtain one unit of that quantity. When we have an equation, the quantities on the left- and right-hand sides of the equality sign in any given law of physics must have the same dimensions (i.e., the same combinations of length, mass, and time).
The main reason we have to put constants in formula of physics is units. To balance dimensions on either side. The dimension of any physical quantity expresses its dependence on the base quantities as a product of symbols (or powers of symbols) representing the base quantities.
As per the principle of homogeneity of dimension, addition subtraction or equality between two quantities of different dimensions are not possible while division and multiplication are possible. With two quantities having same physical dimensions, we can add, subtract, multiply or divide them with no restriction.
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