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A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $$\frac{10}{x}$$. The value of $$x$$ is __________
Correct Answer: 1
1000 small drops coalesce to 1 big drop. Volume conserved: $$1000 \times \frac{4}{3}\pi r^3 = \frac{4}{3}\pi R^3 \Rightarrow R = 10r$$.
Surface energy: $$E = \sigma \times 4\pi r^2 \times n$$ for droplets, $$E_{big} = \sigma \times 4\pi R^2$$.
Ratio = $$\frac{1000 \times r^2}{R^2} = \frac{1000r^2}{100r^2} = 10 = \frac{10}{1}$$.
So $$x = 1$$.
The answer is 1.
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