What is principal of homogeneity of dimensional equation ?

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In a dimentional equation both sides of the equation must have the same units. This is called the homogeneity principle. In Newton's law of universal gravitation we have:

F=G mM / d2 (m,M stand for two different masses)

If the left hand side is in Newtons so the right hand side must also be in Newtons if this is to make sense. The units of mass and distance are set at meters and kilograms to be consistent with Newtons (SI units). This means that the units of G must be Newtons meters2/ kilogram2 for this equation to make sense.

If we use cgs units then the force is in dynes, the mass is in grams and the distance is in centimeters. G must be in units of dynes cm2 / grams 2. This means that the numerical value of G in cgs units is different than in Si units in order to make this work out.

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