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

Options

A. `[(6T)/(rho)(1/a-1/b)]^(1//2)`
B. `[(6T)/(rho)(1/b-1/a)]^(1//2)`
C. `[(rho)/(6T)(1/a-1/b)]^(1//2)`
D. `[(rho)/(6T)(1/b-1/a)]^(-1//2)`

Answer

a

Explanation

Suppose n number of liquid drops are merged equating initial and final volume we have
`v_(i)=v_(t)`
`rarr n xx 4/3 pi a^(3)=4/3 pi b^(3)`
`rarr b=(n)^(1//3)a rarr n =(b/a)^(3)`
initial surface energy `u_(i)=nxx 4pi a^(2)xxS`
final surface energy `u_(f)=4pib^(2)xxS`
change in surface energy
speed of the bigger drop `v=[(6T)/(p)(1/a-1/b)]^(1//2)`