The terminal velocity of a liquid drop of radius 'r falling through air is v. If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air)

Options

A. `sqrt2v`
B. 2v
C. `root(3)(4)v`
D. `root(3)(2) v`

Answer

C

Explanation

Terminal velocity,` V= 2/9 (r^(2)(p-sigma)g)/eta`
Let radius of the smaller drops be 'r* and that of the bigger drop be ‘R’.
If two small drops of same radius combine to form a bigger drop of some radius then,
`4/3 pi R^(3)=4/3 pi r^(3)+ 4/3 pi r^(3)`
`therefore R = (2)^(1/3).r`
`v/V_(1)= r^(2)/((2)^(2/3)r^(2)) [because "critical Velocity" proptor^(2)]`
`therefore V_(1)=3sqrt(4).V`