prove that 1/2 mv²=mgh

by doing dimensional analysis 

LHS 1/2 M V2 =m 1 L 2 t-2

m is mass g acceleration due to gravity h is hieght 

RHS mgh= [m1] [m0 L1 t -2] [m0 L1 t0]

                              [m1 L2 t -2]

so 1/2 m v2 =mgh

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