Question

Mention any two limitations of the dimension analysis.

Answer 1

Hint- The study of the relationship between physical quantities with the help of dimensions and units of measurement is termed as dimensional analysis. With the help of dimension analysis it becomes simple to do mathematical calculations because the only thing we have to do is to keep the dimensions the same.

Step-By-Step answer:
But it has some limitations also major ones are the following:
If an equation is dimensionally correct it does not mean that the equation is correct. Sometimes dimensionally correct equations are also wrong.
For e.g. ${v^2} + 2as{\text{ and }}{v^2} + 5as$ have the same dimensions but they are physically incorrect.
With the help of dimensional analysis we cannot check whether the quantity is scalar or vector
The equation or formula cannot be derived if the physical quantity depends on more than three variables having dimensions
A formula containing trigonometric equation, exponential function, and logarithmic function cannot be derived.

Note- There are seven base SI units. With the help of these seven base units the other units are derived. For example the unit of area is sq. meter and it is derived from the unit of length meter. Similarly the dimensions of the derived quantities are also written in the form of the dimension of the seven base units. The dimensional analysis gives us the formula of the function although it depends whether it is correct or not. So it can be used to cross verify the results of our derived formula. Dimensional analysis can be used as a tool to construct equations that relate non-associated physico-chemical properties.