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

Answer 1

Correct option: (d)

$$\begin{gathered} \mathrm{No}.\mathrm{of}\mathrm{surfaces}\mathrm{of}\mathrm{a}\mathrm{soap}\mathrm{bubble}=2 \\ \mathrm{Increase}\mathrm{in}\mathrm{surface}\mathrm{area}=4\mathrm{\pi }(2\mathrm{r}{)}^2-4\mathrm{\pi }(\mathrm{r}{)}^2=12{\mathrm{\pi r}}^2 \\ \mathrm{Total}\mathrm{increase}\mathrm{in}\mathrm{surface}\mathrm{area}=2\times 12{\mathrm{\pi r}}^2=24{\mathrm{\pi r}}^2 \\ \mathrm{Work}\mathrm{done}=\mathrm{change}\mathrm{in}\mathrm{surface}\mathrm{energy} \\ =\mathrm{S}\times 24{\mathrm{\pi r}}^2=24{\mathrm{\pi r}}^2\mathrm{S} \end{gathered}$$