Question

Which of the following equations cannot be deduced using dimensional analysis?

Answer 1

1. Dimension does not depend on the magnitude of the quantity involved. Therefore, a dimensionally correct equation need not be actually correct.

e.g. :dimension of $\frac{1}{T}$ and $\frac{2\pi }{T}$ are same

2. Dimensional method cannot be used to derive relations other than those involving products of physical parameters.

e.g. :$y=acos(\omega t-kx)$ can not be derived using this method.

3. This method cannot be applied to derive formula if in mechanics a physical quantity depends on more than three physical quantities (mass, length, time).

e.g. :$T=2\pi \sqrt{\frac{I}{mgL}}$cannot be derived by using dimensions.