What are the limitations of dimensional analysis?

unitsandmeasurement
cbse

#1

(i) If a physical quantity depends upon more than three different base quantities, the formula cannot be derived with the help of dimensional analysis.
(ii) Dimensional analysis may not give the formula with true physical relationship, e.g., according to dimensional analysis.
s = ut + 1/2 a${{t}^{2}}$ is the correct relationship.
(iii) Dimensionless constants like 1,2,3,…, e, $\pi $ are not available in the formula derived with the help of dimensional analysis.
(iv) Formula containing trigonometric, exponential functions cannot be derived with the help of dimensional analysis.
(v) This method does not inform about the nature of the derived physical quantity, i.e., whether it is scalar or vector.