While falling through the air, twenty seven droplets having the same radius 1 mm and terminal velocity 10 cms ⁻¹ combine to form a single drop. What is the terminal velocity of the single bigger drop?

Step-by-step solution

Let r be the radius of each small droplet and R be the radius of the single large drop. Since the volume is conserved, we have 27 4 3 r³ = 4 3 R³ . This implies R³ = 27 r³ , so R = 3r . The terminal velocity v of a droplet is given by Stokes' Law as v = 2 9 r² g ( - ) , where is the density of the liquid and is the density of air. From this expression, v r² . Let v₁ be the terminal velocity of the small droplet and v₂ be the terminal velocity of the large drop. Then v₂ v₁ = ( R r )² . Substituting R = 3r , we get v