Physics

State the principle of homogeneity of dimensions. Test the dimensional homogeneity of the following equation:
$$h=h_0+v_0t+\frac {1}{2}gt^2$$


SOLUTION
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 : $$h =[L]$$, dimesion of legth
On right side: $$h_0=[L],  v_0t=[LT^{-1}][T]=[L],  gT^2=[LT^{-2}][T^2]=[L]$$ 
Thus, the dimension on both sides quantities are same. 
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