A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of the energy of the big drop is . The value of is ____.

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Solution

Q.
A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of the energy of the big drop is $\frac{10}{x}$ . The value of $x$ is ____. [2024]

Ans.
(1)

$1000 \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3} \Rightarrow R = 10 r$

Surface energy of 1000 drops $= 1000 \times T \times 4 π r^{2}$

Surface energy of bigger drop $= T \times 4 π R^{2}$

$\frac{S.E. of 1000 drops}{S.E. of Big drop} = \frac{1000 (4 π r^{2}) T}{4 π R^{2} T} = \frac{1000 \times r^{2}}{{(10 r)}^{2}}$

$\Rightarrow \frac{S.E. of 1000 drops}{S.E. of Big drop} = 10 = \frac{10}{x}$

$∴$ $x = 1$

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