125 small water drops of same size fall through air with constant velocity 4 ~cm / s . They coalesce to form a big drop. The terminal velocity of the big drop is

Step-by-step solution

Let a small water drop have radius r and the large coalesced drop have radius R . Volume conservation requires that 125 small drops equal one large drop: 125 4 3 r^3 = 4 3 R^3 . Simplifying yields 125 r^3 = R^3 , so R = 5r . For a spherical drop falling through a viscous medium, terminal velocity v_t follows Stokes' Law, v_t = 2 r^2 g ( - ) 9 , implying v_t r^2 . Let v_ t,big and v_ t,small denote the terminal velocities of the large and small drops, respectively. The ratio is v_ t,big v_ t,small = R^2 r^2 = (5r)^2