to prove: s=ut+1/2at2
proof:
L.H.S. :- DIMENSION OF [S] = [L]
RHS:- DIMENSSION OF u =[LT-1]
DIMENSSION OF t = [T]
DIMENSSION OF a = [LT-2 ]
THEREFORE DIMENSSION OF R.H.S. ut+1/2at2 = [LT-1] . [T]+[LT-2 ] [T] 2 {WE IGNORE 1/2 SINCE 1/2 IS DIMENSSIONLESS}
= [L] + [L] = [L] { [L]+[L] = [L] AND NOT 2[L}
= DIMENSSION OF L.H.S
SINCE DIMENSSION OF L.H.S = DIMENSSION R.H.S.
HENCE PROOVED ...........................