COMMENT- THE DIMENSIONAL ANALYSIS FAILS TO DERIVE THE RELATION INVOLVING MORE THAN THREE INDEPENDENT FACTORS.

Asked by Karishma Sayyad | 9th May, 2014, 06:05: PM

Expert Answer:

Dimensional analysis fails to derive a relationship, when a physical quantity depends upon more than three physical quantities.

This is due to the fact that we can get at most three equations by comparing the powers of three fundamental units (M, L and T). Hence, according to the theory of algebraic equations, this method can be used to find the value of three unknown quantities only.

Also, this method cannot be used to derive the relations such as, S = ut +1/2at2, v2 – u2 = 2as, etc by the usual method. Such relations are called composite relations (the relation, which have two or more than two terms on one side of the relation).

In   composite relations, each term has the same dimensions. It is because; only like quantities can be added and subtracted from one another.  Such relations can be derived in parts. Even while deriving such relations in parts, it does not tell about the nature of sign (plus or minus) connecting the various terms in the relations.

Answered by Komal Parmar | 12th May, 2014, 11:42: AM