A big water drop is formed by the combination of n small water drops of equal radii. The ratio of the surface energy of n drops to the surface energy of the big drop is

Step-by-step solution

Volume of big drop = n (Volume of small drop) 4 3 π R 3 = n . 4 3 π r 3 R 3 = n r 3 R = n 1 3 . r E 2 = s u r f a c e e n e r g y o f n d r o p s = n × 4 π r 2 × T E 1 = s u r f a c e o f e n e r g y o f b i g d r o p = 4 π R 2 T ∴   E 2 E 1 = n r 2 R 2 = n r 2 ( n 1 3 . r ) 2 = n r 2 n 2 3 . r 2 ∴   E 2 E 1 = n 1 3 = n 3   : 1