A large number of liquid drops each of radius r coalesce to from a single drop of radius R . The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given, surface tension of liquid T , density ρ )

Question

A large number of liquid drops each of radius r coalesce to from a single drop of radius R . The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given, surface tension of liquid T , density ρ ), T ρ 1 r - 1 R, 2 T ρ 1 r - 1 R, 4 T ρ 1 r - 1 R, 6 T ρ 1 r - 1 R

MARKS App · Accepted Answer

n 4 3 π r 3 = 4 3 π R 3 n = R 3 r 3 Δ U = n 4 π r 2 T - 4 π R 2 T = 4 π T n r 2 - R 2 = 4 π T R 3 r 2 r 3 - R 2 ∴ Energy released, U = 4 π T R 3 [ 1 r − 1 R ] If this energy is converted into kinetic energy then 1 2 m v 2 = 4 π R 3 T [ 1 r − 1 R ] 1 2 × [ 4 3 π R 3 ρ ] v 2 = 4 π R 3 T [ 1 r − 1 R ] v = 6 T ρ [ 1 r − 1 R ]

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