Two identical drops of water are falling through air with a steady speed of 'V' each. If the drops coalesce to form a single drop, what is the new terminal velocity?

Explanation

From conservation of mass,
`(4)/(3)piR^(3)xxrho=(4)/(3)pir^(3)xxrho+(4)/(3)pir^(3)xxrho`
or `R=(2^(1//3))r. and V_(T)propr^(2)` (stokes law)
`(V^(1))/(V)=(R^(2))/(r^(2))=2^(2//3) therefore V^(1)=2^(2//3)V`.