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uses of dimensional analysis?

(i)  To check the correctness of an equation

An equation is correct only if the dimensions of each term on either side of the equation are equal.In this case the equation is dimensionally correct ;but, may or may not be the correct equation for the physical quantity.If the homogenity of dimensions does not hold good, the equation is definitely incorrect.

(ii) To convert a unit from one system into another

Since a physical quantity is expressed in terms of appropriate units of the same nature in all systems, the dimensions should remain the same eventhough the number indicating its magnitude may differ.If a physical quantity of dimensions a , b, c in mass, length and time respectively has magnitude n1 and n2 in two systems having  fundamental units M1,L1,T1 and M2, L2, T2, respectively then,

                                           n1M1aL1bT1c = n2M2aL2bT2c
                                                            n2 = n1(M1/M2)a (L1/L2)b (T1/T2)c

(iii) To derive the correct relationship between physical quantities

When one physical quantity depends on several quantities, then the relationship between the quantities can be derived using dimensional method.

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