Question

State the principle of homogeneity of dimensions. Test the dimensional homogeneity of the following equation:
$h=h_0+v_{0}t+\frac{1}{2}g{t}^2$

Answer 1

The principle of homogeneity states that the dimensions of each the terms of a dimensional equation on both sides are the same.

Using this principle the given equation will have same dimension on both sides.

On left side : $h=\left[L\right]$, dimesion of legth

On right side: $h_0=\left[L\right],v_{0}t=\left[L{T}^{-1}\right]\left[T\right]=\left[L\right],g{T}^2=\left[L{T}^{-2}\right]\left[T^2\right]=\left[L\right]$

Thus, the dimension on both sides quantities are same.