Question

What are the limitation of dimensional analysis?​

Answer 1

★ LIMITATIONS OF DIMENSIONAL ANALYSIS:-

→ The value of the constant of proportionality cannot be determined.

→ If the constant of proportionality has dimensions and its nature is not known, dimensional analysis cannot be applied.

→ Dimensional analysis cannot be applied to relations involving trigonometric, logarithmic and exponential functions.

→ The relation connecting a set of physical quantities can be deduced only if the relation is in the form of a product.

→ If the number of quantities on which a physical quantity depends exceeds the number of fundamental units involved.

→ It is not possible to obtain an expression relating them.

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.