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  • What is the change in surface energy, when a mercury drop of radius R splits up into 1000 droplets of radius r

What is the change in surface energy, when a mercury drop of radius R splits up into 1000 droplets of radius r?

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\begin{aligned} &\text { Volume of one drop }=\text { Volume of } 1000 \text { droplets }\\ &\therefore \frac{4}{3} \pi R^{3}=100\left(\frac{4}{3} \pi r^{3}\right)\\ &\therefore R^{3}=1000 r^{3} \quad \therefore r=\frac{R}{10} \end{aligned}

\begin{aligned} &\text { Change in surface area }\\ & \ \ \ \ =1000.4 \pi r^{2}-4 \pi R^{2}\\ & \ \ \ \ =4 \pi\left[1000 \times \frac{R^{2}}{100}-R^{2}\right]\\ &\therefore \ \ \ d A=4 \pi\left[10 R^{2}-R^{2}\right]=36 \pi R^{2} \end{aligned}

\\\text{So, Workdone = Change in Surface energy } =\mathrm{T} \Delta \mathrm{A}=(40-4) \Pi \mathrm{R}^{2} \mathrm{T} \\ \text{Change in Surface energy }$=36 \Pi \mathrm{r}^{2} \mathrm{T}$

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lovekush

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