If the time period (T) of vibration of a liquid drop depends on surface tension (S), radius of the drop and density (ρ) of the liquid, then the expression of T is

Let T ∝ Sxryρzby substituting the dimension of [T] = [T]S = MT−2, r = L, ρ = ML−3and by comparing the power of both the sidesx = −12,  y  =  32 ,   Z = 12so T ∝ ρr3S ⇒ T = kρr3S