A large number of liquid drops each of radius a coalesce to form a single spherical drop of radius b. The energy released in the process is converted into kinetic energy of the big drop formed. The speed of big drop will be

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$\sqrt{\frac{6 T}{ρ} [\frac{1}{a} - \frac{1}{b}]}$

$\sqrt{\frac{4 T}{ρ} [\frac{1}{a} - \frac{1}{b}]}$

$\sqrt{\frac{8 T}{ρ} [\frac{1}{a} - \frac{1}{b}]}$

$\sqrt{\frac{5 T}{ρ} [\frac{1}{a} - \frac{1}{b}]}$

answer is A.

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Detailed Solution

$N (\frac{4}{3} {πa}^{3}) = \frac{4}{3} {πb}^{3} \Rightarrow N = \frac{b^{3}}{a^{3}} A_{i} = N (4 {πa}^{2}) = \frac{4 {πb}^{3}}{a} A_{f} = 4 {πb}^{2} ΔA = A_{i} - A_{f} = 4 {πb}^{2} (\frac{b}{a} - 1) W = T (ΔA) = 4 {πb}^{2} (\frac{b}{a} - 1) T = \frac{1}{2} {mv}^{2} = \frac{1}{2} (\frac{4}{3} {πb}^{3} ρ) v^{2} On solving, we get v = \sqrt{\frac{6 T}{ρ} (\frac{1}{a} - \frac{1}{b})}$