Question

On the basis of dimensional equation, the maximum number of unknowns that can be found, is
A. One
B. Two
C. Three
D. Four

Answer 1

Hint: The number of unknowns that can be found for any physical quantity while performing the dimensional analysis and writing the dimensional equation will be the same as that of the number of the physical parameters being used for that particular physical quantity.

Complete step by step answer:
So, if we have to define the dimension for any physical quantity then we perform this dimensional analysis by taking three basic and fundamental parameters into account. They are mass $$\left[M\right]$$, length $\left[L\right]$, and time $\left[T\right]$.
Hence the maximum number of the unknowns that can be found, on the basis of the dimensional equation of a particular physical quantity are three.

So, the correct answer is “Option C”.

Note: The dimensional equation is written in the terms of the fundamental parameters of that particular physical quantity. So, the dimensional equation is formed when we equate the particular physical quantity with its dimensional formula. Hence the dimensional equation helps in expressing the particular physical quantity in the terms of fundamental or base parameters of the quantity.
There is some application of the dimensional equation. From the help of a dimensional equation we can find some useful results. So, the applications of the dimensional equation of a particular physical quantity are as follows-
1. Conversion of one unit from one system to another.
2. To check the correctness of any particular equation. Hence to check that the particular given equation we can take the help of the dimensional formula.
3. To derive the relationship between different physical quantities which are involved in some process. Hence the derivation of the formula involved in a phenomenon can be found with the help of the dimensional analysis.