A large number of liquid drops each of radius a are merged to form a single sperical drop of radius b the energy released in the process is converted
A large number of liquid drops each of radius a are merged to form a single sperical drop of radius b the energy released in the process is converted into kinetic energy of the bigh drop formed the speed of the bigh drop is
[p density of liquid T= surface tension of liquid]
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)`
1 Answers
Correct Answer - a
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)`