Question

Eight spherical rain drops of equal size are falling vertically through air with a terminal of `0.10 ms^(-10`. What should be the velocity if these drops were to combine to form one large spherical drop?

Answer 1

Ler r be the radius of each of the small rain drop and R be the radius of big rain drop formed.
As, volume of big drop = 8 xx volume of each small drop
`:. 4/3 pi R^(3) = 8 xx 4/3 pi r^(3) or R=2r`
Let terminal velocity of small drop be `upsilon_(1)` and of big drop be `upsilon_(2)`
As terminal velocity ,
`upsilon = (2 r^(2) (rho-sigma)g)/(9 eta) or upsilon prop r^(2)`
`:. (upsilon_2)/(upsilon_1) = (R^2)/(r^2)`
or `upsilon_(2) = upsilon_(1) xx (R^2)/(r^2) = 0.1 ((2r)/(r ))^(2)`
`=0.1 xx 4 = 0.4 ms^(-1)`.