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Question

Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution in S, the work done in the process is (a) 8 π r2 S (b) 12 π r2 S (c) 16 π r2 S (d) 24 π r2 S

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Solution

Correct option: (d) $\mathrm{No}.\mathrm{of}\mathrm{surfaces}\mathrm{of}\mathrm{a}\mathrm{soap}\mathrm{bubble}=2\phantom{\rule{0ex}{0ex}}\mathrm{Increase}\mathrm{in}\mathrm{surface}\mathrm{area}=4\mathrm{\pi }\left(2\mathrm{r}{\right)}^{2}-4\mathrm{\pi }\left(\mathrm{r}{\right)}^{2}=12{\mathrm{\pi r}}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{Total}\mathrm{increase}\mathrm{in}\mathrm{surface}\mathrm{area}=2×12{\mathrm{\pi r}}^{2}=24{\mathrm{\pi r}}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{Work}\mathrm{done}=\mathrm{change}\mathrm{in}\mathrm{surface}\mathrm{energy}\phantom{\rule{0ex}{0ex}}=\mathrm{S}×24{\mathrm{\pi r}}^{2}=24{\mathrm{\pi r}}^{2}\mathrm{S}$

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