64 rain drops of the same radius are falling through air with a steady velocity of 0.5 ~cm ~s ⁻¹ . If the drops coalesce, the terminal velocity would be

Step-by-step solution

Let r be the radius of each small drop and v be its terminal velocity. The terminal velocity of a spherical drop is given by Stokes Law as v = 2 9 r^2( - )g , where is the density of the drop, is the density of air, and is the coefficient of viscosity. This implies v r^2 . When n = 64 drops coalesce into a single large drop of radius R , the volume remains constant. Thus, 4 3 R^3 = n 4 3 r^3 , which gives R^3 = n r^3 , or R = n^ 1/3 r . Substituting n = 64 , we get R = (64)^ 1/3 r = 4r . Let V be the terminal veloc