Eight equal drops of water are falling through air with a steady velocity of 10 `cms^(-1)`. If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is

Explanation

Let R= radius of bigger drop
r= radius of each small drop
Equate volumes when the 8 drops merge into one.
`:. (4)/(3) pi R^(3) = 8 xx (4)/(3) pi r^(3)`
`:. R= 2r`
Since terminal velocity `V= (2)/(9) ((rho -sigma) r^(2)g)/(eta)`
`:. ("Terminal velocity of bigger drop")/("Terminal velocity of smaller drop")= (R^(2))/(r^(2))`
or `(V)/(10) = ((2r)/(r ))^(2) = 4 or V= 40 cm s^(-1)`