Units and Dimensions LIMITATIONS OF DIMENSIONAL ANALYSIS
Limitations of Dimensional Analysis Dimensional analysis has no information on dimensionless constants. lf a quantity is dependent on trigonometric or exponential functions, this method cannot be used In some cases, it is difficult to guess the factors while deriving the relation connecting two or more physical quantities.
This method cannot be used in an equation containing two or more variables with same dimensions. lt cannot be used if the physical quantity is dependent on more than three unknown variables. This method cannot be used if the physical quantity contains more than one term, say sum or difference of two terms
Even if a formula is dimensionally correct, it may still be incorrect. This method does not inform about the nature of the derived physical quantity, i.e., whether it is scalar or vector.
Nikhil Mishra is an engineer and has been a Faculty of Physics in some of the most premier institutes of the country and has been involved