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

Step-by-step solution

Let radius of big drop =R Radius of small drop =r Number of small drops, n=1000 In this process, the volume remains same V_f=V_i 4 3 R^3=n ( 4 3 r^3 )R^3=1000 r^3 R=10 r ...(i) Initial surface area, A₁=n 4 r^2 Final surface area, A₂=4 R^2 Now, increase in surface area, A=A₂-A₁=4 [R^2-n r^2 ] We know that, surface energy, SE = TA [where, T= surface tension of liquid] According to question, SE _f SE _i = TA ₂ TA ₁ = 4 R^2 n (4 r^2 ) = R^2 1000 r^2 [From Eq. (i)] = (10 r)^2 1000 r^2 = 100 r^2 1000 r^2 = 1 10 or 1: 10