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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
Options
8 π r2 S
12 π r2 S
16 π r2 S
24 π r2 S
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Solution
\[\text{ No . of surfaces of a soap bubble } = 2\]
\[\text{ Increase in surface area }= 4\pi(2r )^2 - 4\pi(r )^2 = 12 \pi r^2 \]
\[\text{ Total increase in surface area }= 2 \times 12 \pi r^2 = 24 \pi r^2 \]
\[\text{ Work done = change in surface energy } \]
\[ = S \times 24 \pi r^2 = 24 \pi r^2 S\]
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