v = 1/2l √T/m
Write the dimensions on either sides, we have
L.H.S. = v =[T-1] = [M0L0T-1]
R.H.S. = 1/2l = √T/m
(As 1/2 has no dimensions)
Tension is force and m is mass per unit length,so
As, L.H.S. = R.H.S., dimensionally. therefore, formulae is correct.