Question

If $T$ is the surface tension of soap solution, the amount of work done in blowing a soap bubble from a diameter $D$ to a diameter $2D$ is

• A. $2\pi D^{2}T$
• B. $4\pi D^{2}T$
• C. $6\pi D^{2}T$
• D. $8\pi D^{2}T$

Answer 1

The correct option is C $6\pi D^{2}T$

Work done, $W=$ (increase in surface area) $\times$ surface tension
$W=2\times [4\pi {\left(\frac{2D}{2}\right)}^2-4\pi {\left(\frac{D}{2}\right)}^2]\times T$
(Since for soap bubble, there are two free surfaces)
$=2\times (4\pi D^2-\pi D^2)T=6\pi D^{2}T$