Question 107 of 192

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 __________

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Answer: 1

$\begin{aligned} 1000 \frac{4}{3} \pi r^3 & =\frac{4}{3} \pi R^3 \\ 10 r & =R \\ R & =10 r\end{aligned}$
$\begin{aligned} \frac{\text { S.E. of } 1000 \text { drops }}{\text { S.E. of Big drop }} & =\frac{1000\left(4 \pi \mathrm{r}^2\right) \mathrm{T}}{4 \pi \mathrm{R}^2 \mathrm{~T}} \\ & =\frac{1000 \times \mathrm{r}^2}{(10 \mathrm{r})^2}=10=\frac{10}{\mathrm{x}} \\ \therefore \quad x & =1\end{aligned}$