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

Question

If the time period ( T ) of vibration of a liquid drop depends on surface tension ( S ) , radius ( r ) of the drop and density ( ρ ) of the liquid, then the expression of T is, T = k ρ r 3 / S, T = k ρ 1 / 2 r 3 / S, T = k ρ r 3 / S 1 / 2, None of these

MARKS App · Accepted Answer

Let T ∝ S x r y ρ z by substituting the dimension of [ T ] = [ T ] [ S ] = [ M T − 2 ] , [ r ] = [ L ] , [ ρ ] = [ M L − 3 ] and by comparing the power of both the sides x = − 1 / 2 , y = 3 / 2 , z = 1 / 2 so T ∝ ρ r 3 / S ⇒ T = k ρ r 3 S

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