Question

what is the limitations of dimension rule

Answer 1

You can't predict the constant value involved in a physical equation.

For example in energy is directly proportional to frequency relation you can't predict the value of hedge only with dimensional analysis.

Answer 2

Following are the few $\textbf{limitations of Dimensional Analysis }$:

1) It doesn't enables us to determine the value of proportionality constant, which may be a pure number or dimensionless ratio.

2) It can't be used to derive relationship involving trigo. or exponential function.

3) It fails to derive a relationship which guarantee correctness of a relation because many physical quantities have same dimensions.