Question

If $T$ is surface tension of the soap solution, then the amount of work done in blowing a soap bubble from diameter $D$ to 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 $6\pi D^{2}T$

We know,
Work done in blowing soap bubble,
$W=T\times 2\Delta A$
$W=T\times 2\times 4\pi (R_2^2-R_1^2)$
$=8\pi T({\left(\frac{D_2}{2}\right)}^2-{\left(\frac{D_1}{2}\right)}^2)$
$=2\pi T(D_2^2-D_1^2)$
$=2\pi T\left(\right(2D{)}^2-D^2)$
$=6\pi T{D}^2$