Question

What are the limitations of dimensional analysis?

Answer 1

Dimension-ally correct equation is sometimes incorrect because it doesn’t take into account dimensionless constants like numbers.

For e.g : v^2+2as and v^2+5as have same dimensions but they are physically incorrect.

It does not test whether a physical quantity is a scalar or a vector.

It cannot derive relation or formula if a physical quantity depends upon more than three factors having dimensions.

It cannot derive a formula containing trigonometric function, exponential function, and logarithmic function.

It cannot derive a relation having more than one part in an equation.