state principle of homogeneity of dimebsions
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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
0
t=
[LT
−1
][T]=
[L],gT
2
=
[LT
−2
][T
2
]=
[L]
Thus, the dimension on both sides quantities are same.
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