' n ' small water drops of same size (radius r ) fall through air with constant velocity V. They coalesce to form a big drop of radius R. The terminal velocity of the big drop is

Step-by-step solution

Terminal velocity for a spherical drop follows Stokes' Law: V_t = 2 9 ( - )g r^2 , where r is the radius. This simplifies to V_t r^2 , or V_t = K r^2 for constant K . When n identical drops coalesce, volume conservation requires n r^3 = R^3 , where R is the radius of the large drop. Solving gives R = n^ 1/3 r . The terminal velocity of the large drop is V_R = K R^2 = K (n^ 1/3 r)^2 = K n^ 2/3 r^2 . Since the small drop has V = K r^2 , the ratio is V_R V = n^ 2/3 , so V_R = V n^ 2/3 . The correct choice is Option A