## Saturday, February 4, 2017

### Uses and Applications of Dimensional Analysis Video Lesson

Dimensional formula is a representation of a physical quantity in terms of fundamental quantities. We represent mass with M, length with L and time with T in dimensional formula. Dimensional analysis can be done basing on principle of homogeneity and according to it the dimensions of left hand side and right hand side of the equation has to be equal. It mean to tell us that we can add or subtract only similar physical quantities but not dissimilar ones. Using the dimensional formula and analysis, we can convert a physical quantity from one system of unit to other.

Conversion of physical Quantity from one system to other

For example we can that the energy is measured in the unit joule in SI system and erg in CGS system. Because they are the units of same physical quantity in different system of units, they shall be having some relation between them. We can find that relation using the principle of homogeneity.

Checking the correctness of given equation

We can also use the dimensional analysis to check the correctness of a given equation. We have so many equations in physics and before they are correct as per the subject, they have to be correct conceptually. That can be verified using the dimensional analysis. Here we are depending on the concept of principle of homogeneity and according to it LHS and RHS of a equation shall have same dimensions of the physical quantities. If the sum of left hand side physical quantities is velocity then the right hand side sum or difference of the terms shall also be the velocity. In the other sense, we are adding or subtracting physical quantities of the same nature but not different.

Finding Relation among Physical Quality

We can also use dimensional analysis to find the relation between physical quantities basing on principle of homogeneity. We will simple equate the dimensions of left hand side of the equation with the right hand side equation so that we will be getting mathematical equations and by solving them, we can get the dimensions of the physical quantities. Here we will be able to find only the relation but we can not find the proportional constant values using this method. This is one limitation of the dimensional analysis.