If energy (B), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

We know that, surface tension (S)= Force [F] Length [L]so,           [S]=MLT−2[L]=ML0T−2Energy (E) = Force x Displacement ⇒ [E] = [ML2T-2]Velocity (v)= Displacement  Time ⇒[v]=LT−1As,         S∝EavbTcwhere, a, b and c are constants.From the principle of homogeneity,                                 [LHS] = [RHS]⇒               [ML0T-2] = [ML2T-2]a[LT-1]b[T]c⇒               [ML0T-2] = [MaL2a + bT2a - b + c]Equating the power on both sides, we get                    a = 1, 2a + b ⇒ 0 ⇒ b = - 2and      - 2a - b + c = - 2⇒                      c = (2a + b) - 2 = 0 - 2 = - 2So,                  [S] = [Ev-2T-2]