Dimensional formula checking for v²= 2 g h

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» Checking dimensional correctness for v²= 2 g h

LHS = v² = [L T ^-1]² = [L² T ^-2]

RHS = 2 g h = 2 [L T ^-1][L] = [L² T^-2]

             »LHS = RHS

So, the LHS= RHS. 

HENCE, the given formula is dimensionally correct. 

» Checking dimensional correctness for v = u+ at

LHS = v = [L T ^-1] 

RHS = u + at=  [L T ^-1] + [L T^-2][T] 

                     = [L T^-1]

             »LHS = RHS

So, the LHS= RHS. 

HENCE, the given formula is dimensionally correct. 

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