One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

Step-by-step solution

Let r be the radius of each small drop and R be the radius of the big drop. Since volume remains constant during the combination of drops: 4 3 R^3 = 1000 4 3 r^3 R = 10r Initial total surface energy of 1000 drops is: E_i = 1000 4 r^2 T Final surface energy of the big drop is: E_f = 4 R^2 T = 4 (10r)^2 T = 100 4 r^2 T The ratio of final surface energy to the total initial surface energy is: E_f E_i = 100 4 r^2 T 1000 4 r^2 T = 1 10 The ratio is 1 : 10 . Answer: 1 : 10