Question

$64$ spherical rain drops of equal size are falling vertically through air with a terminal velocity $1.5{ms}^{-1}$. If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is:

• A. $8{ms}^{-1}$
• B. $16{ms}^{-1}$
• C. $24{ms}^{-1}$
• D. $32{ms}^{-1}$

Answer 1

The correct option is C $24{ms}^{-1}$

Terminal velocity is directly proportional to the square of the radius of the spherical body.

Since mass is conserved and density remains same, upon coalesceing, the volumes will add up.

Thus, volume of bigger drop $=$ 64 times the volume of each small drop. Since volume is directly proportional to cube of radius, this implies that the radius of the big drop is 4 times the radius of each small drop.

Therefore, terminal velocity of the big drop is 4 square $=$ 16 times the terminal velocity of each small drop $=1.5\times 16=24m{s}^{-1}$