question_answer

A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R. An Engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is (T = surface tension, \[\rho \] = density)                                                                      [JEE ONLINE 19-05-2012]

A)       \[{{\left[ \frac{T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]         

B) \[{{\left[ \frac{6T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]

C) \[{{\left[ \frac{3T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]

D)      \[{{\left[ \frac{2T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]

Correct Answer: B

Solution :

[b] When small droplets coelesce to form a bigger drop, energy released in this process is given by,

Where, R = radius of big drop r = radius of small drop T = surface tension

According to question