A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

Solution

Physics sir · 3 steps

Volume stays the same when drops merge, so get the big radius from volume, then compare total surface areas.

1. Volume is conserved. Let each droplet have radius r and the big drop radius R. The water only rearranges, so 4/3π R³ = 1000 × 4/3π r³. This gives R³ = 1000 r³, so R = 10r.
2. Surface energy follows area. Surface energy is E = T × A, where T is the surface tension and A is the total surface area. T does not change, so the energy ratio equals the area ratio.

   E_(big)/E_(small, total) = (4π R²)/(1000 × 4π r²) = (10r)²/(1000 r²) = 100/1000 = 1/10

3. So. The total surface energy becomes 1/10th of its original value, which is option (b). The energy that disappears is released, mostly as heat.

The idea to keep. When n drops merge, volume is conserved, so R = n^(1/3) r. Total area, and so surface energy, changes by a factor n^(-1/3). Merging always lowers surface energy.

Answer from the NTA final answer key. Solution by PrepWiser.