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A big drop is formed by coalescing 1000 small identical drops of water. If $$E_1$$ be the total surface energy of 1000 small drops of water and $$E_2$$ be the surface energy of single big drop of water, the $$E_1 : E_2$$ is $$x : 1$$, where $$x$$ = ________.
Correct Answer: 10
Volume of 1000 small drops = volume of big drop.
$$1000 \times \frac{4}{3}\pi r^3 = \frac{4}{3}\pi R^3 \Rightarrow R = 10r$$.
$$E_1 = 1000 \times 4\pi r^2 \times T$$
$$E_2 = 4\pi R^2 \times T = 4\pi (10r)^2 T = 400\pi r^2 T$$
$$\frac{E_1}{E_2} = \frac{1000 \times 4\pi r^2 T}{400\pi r^2 T} = \frac{4000}{400} = 10$$
So $$E_1 : E_2 = 10 : 1$$, meaning $$x = 10$$.
Therefore, the answer is $$\boxed{10}$$.
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