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

Answer 1

\[\text{ No . of surfaces of a soap bubble } = 2\]

\[\text{ Increase in surface area }= 4\pi(2r )^2 - 4\pi(r )^2 = 12 \pi r^2 \]

\[\text{ Total increase in surface area }= 2 \times 12 \pi r^2 = 24 \pi r^2 \]

\[\text{ Work done = change in surface energy } \]

\[ = S \times 24 \pi r^2 = 24 \pi r^2 S\]