A liquid drop having surface energy E is spread into 729 droplets of same size. The final surface energy of the droplets is

Step-by-step solution

Surface Energy Transformation of Liquid Droplets Let R be the radius of the original liquid drop, with surface area A₁ = 4 R^2 and initial surface energy E = A₁ , where is the surface tension. The drop is divided into 729 smaller droplets of equal size. By conservation of volume, the total volume remains unchanged. Volume of original drop: 4 3 R^3 Volume of one small droplet: 4 3 r^3 Equating total volumes: 4 3 R^3 = 729 4 3 r^3 Simplifying: R^3 = 729r^3 R = 9r r = R 9 The surface area of one small droplet is a = 4