EduHarsha - A Bridge In Your Journey Of Education

Dear Mathematics Lovers,

We will publish EduHarsha posts on mathematics with the name EduHarsha Mathematics Magic. You can expect several posts covering all the topics of mathematics which are included in higher secondary board.

 Please stay tuned and wait for the exciting journey to start.

Regards,
Pranava

A physical equation is dimensionally correct if each component on either side of the equation hold the same dimension. This principle of dimensional homegeneity of each component of a physical equation is called principle of homogeneity of dimensions. In simple words, a physical quantity can be added with or subtracted from or be compared (establishing equality and/or inequality) with another physical quantity only when they are dimensionally similar.

Let us take example of v = u + at. 
Dimension of v i.e. final velocity = [LT^-1]
Dimension of u i.e. initial velocity = [LT^-1]
Dimension of at which is multiplication of a i.e. accelaration [LT^-2] and t i.e. time [T] = [LT^-2][T] = [LT^-1]

As three components of the equation have the same dimension, the equation is dimensionally correct. We all know that this equation is physically correct. However even a wrong equation like v =u + 2at can be dimensionally correct with dimension of each component being [LT^-1].

Therefore we can not conclude that an equation is correct if all its components are dimensionally homogeneous. However if all the components are not dimensionally homogeneous, we can easily conclude that equation can not be correct. Homogeneity of dimensions is not alone sufficient condition for the equation to be correct but it is a necessary condition. We can use this principle as a quick and first check for separating wrong equations and possibly correct equations.