A large number of liquid drops each of radius r coalesce to form a single drop of the 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 the liquid T , density ρ )

Step-by-step solution

n × 4 3 π r 3 = 4 3 π R 3 ∴   n = R 3 r 3     . . . . . i K E = U i - U f = n × 4 π r 2 T - 4 π R 2 T = 4 π T ( n r 2 - R 2 ) = 4 π T R 2 R r - 1 from i 1 2 4 3 π R 3 · ρ υ 2 = 4 π T R 2 R r - 1 R ρ υ 2 6 = T R r - 1 ρ 6 υ 2 = T 1 r - 1 R υ = 6 T ρ 1 r - 1 R