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Question
What are the limitations of dimensional analysis?
Solution
(1) This method gives no information about the dimensionless constants in the formula. Like 1, 2,7i, e, etc. ie they can not be determined using this analysis.
(2) This method can not decide whether the given quantity is a scalar or a vector.
(3) Using this method one cannot derive relations involving trigonometric, exponential, and logarithmic functions.
(4) It cannot be applied to an equation involving more than three physical quantities.
(5) It can be used to check whether a given physical relation is dimensionally correct or not. The physical correctness can not be checked using this
For example:
s = ut + `1/3` at² is dimensionally correct were as physically not correct, as the correct equation is s = ut + `1/2`at².
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