Limitations of Dimensional Analysis.

 (1) Dimensions are not unique. Two Physical Quantities can have same dimensions. For example torque and Work Done.

(2) Dimensions of [K] such as (1/2), 1 or 2p etc. cannot be deduced by dimensional analysis.

(3) The method of dimensions can not be used to derive relations other than product of power functions. For example,

s=ut+(1/2)at² or y = a sinwt

cannot be derived by using dimensional analysis.

(4) The method of dimensions cannot be applied to derive formula if in mechanics a physical quantity depends on more than 3 physical quantities as then there will be less number (= 3) of equations than the unknowns (>3).

(5) Even if a physical quantity depends on 3 physical quantities, out of which two have same dimensions, the formula cannot be derived by theory of dimensions