Question

State uses of dimensional analysis

Answer 1

Hint: We can say that the study of the relationship between physical quantities and units of measurement is called dimensional analysis and by using this definition we will state various uses of dimensional analysis and we will also state its importance.

Complete step-by-step answer:
Now, in the question we are asked to mention the uses of dimensional analysis, so first of all we will define dimensional analysis as,
“The study of the relationship between physical quantities and units of measurement is called dimensional analysis.”
Now, dimensional analysis helps us study the nature of objects mathematically. It also helps us in keeping the units the same and helps us in performing the calculations smoothly.
Dimensional analysis can also be used to check the correctness of physical quantity. For e.g.: let us assume that we don’t know that $\text{speed}={\displaystyle \frac{\text{distance}}{\text{time}}}$ and it’s dimensional formula is $m/s\Rightarrow L{T}^{-1}$, so now If we want to check whether we are correct or not then we can keep the dimensional formulas of individual quantities and then we can derive the formula. In this dimensional analysis it is useful to check whether the dimensions we have taken are correct or not.

Additional information:
Dimensional analysis is also called the Factor Label Method or Unit Factor Method because we use conversion factors to get the same units. The principle of homogeneity of dimensional analysis also states that dimensions of each term of a dimensional equation should be the same.

Note: Dimensional analysis and dimensional formulae have key importance in physics as they help us in deriving the dimensions of unknown quantities also. Dimensional analysis is also used to derive formulas of new quantities in dimensional form as well as MLT form. So, each student must learn how to check the dimensions of any quantity.