Question

three limitations of dimensional analysis​

Answer 1

Answer:

Although dimensional analysis is very useful it can’t lead us too far as,

1) If dimensions are given, physical quantity may not be unique as many physical quantities have same dimensions. For example if the dimensional formula of a physical quantity is [ML1T−2] it may be work or energy or torque.

2) Numerical constant having no dimension (K) such as (1/2), 1 or 2π etc. can’t be deducted by the methods of dimensions.

3) The method of dimension can’t be used to derive relations other than product of power functions. For example, s=ut+12at2 (or) y=asinωt can’t be derived by using this theory. However, the dimensional correctness of these can be checked.

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.