Question

What is mean by dimensional homogeneity?

Answer 1

Dimensional homogeneity is the quality of an equation having quantities of the same dimension on both sides. A valid equation in physics must be homogeneous, since equality cannot apply between quantities of different nature. This can be used to spot errors in formula or calculations.
For example, let us take the simple equation F = ma.
Dimension of force is $\left[M\right]\left[L\right][T{]}^{-2}$.
Dimension of mass is $\left[M\right]$.
Dimension of acceletation is $\left[L\right][T{]}^{-2}$.
So, the dimension of mass times acceleration is $\left[M\right]\left[L\right][T{]}^{-2}$, which is the same as that of force. This equation is dimensionally homogeneous.