Question

Air is pushed into a soap bubble of radius $r$ to double its radius. If the surface tension of the soap solution is $S$, the work done in the process is

• A. $8{\pi }^{2}rS$
• B. $12{\pi }^{2}rS$
• C. $16{\pi }^{2}rS$
• D. $24\pi r^{2}S$

Answer 1

The correct option is D $24\pi r^{2}S$

No. of surface of soap bubble$=2$

Increase in surface area$=4\pi (2r{)}^2-4\pi (r{)}^2$

$=12\pi r^2$

Total increase in surface area$=2\times 12\pi r^2$

$=24\pi r^2$

Work done$=$change in surface energy

$=5\times 24{\pi }^2$

$=24\pi r^{2}s$

$\therefore$ Work done$=24\pi r^{2}s$.