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A big drop is formed by coalescing 1000 small identical drops of water. If E1 be the total surface energy of 1000 small drops of water and E2 be the surface energy of single big drop of water, then E1: E2 is x: 1 where x = _____.

1. 10
2. 100
3. 1
4. 1000

Correct answer: 10

Solution

The surface energy of a drop is proportional to its surface area, which scales with the square of the radius. When 1000 small drops coalesce into one larger drop, the total surface area decreases, leading to a reduction in surface energy. Specifically, the ratio of the surface energy of the small drops to that of the big drop is 10:1, as the surface area of the big drop is 10 times that of each small drop.

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