Question

The amount of work done is blowing a soap bubble such that its diameter increases from $d$ to $D$ is ($S=$ surface tension of the solution) :

• A. $2\pi (D^2-d^2)S$
• B. $\pi (D^2-d^2)S$
• C. $4\pi (D^2-d^2)S$
• D. $8\pi (D^2-d^2)S$

Answer 1

The correct option is A $2\pi (D^2-d^2)S$

Change in surface area

$=2\times 4\pi [{\left(\frac{D}{2}\right)}^2-{\left(\frac{d}{2}\right)}^2]=2\pi (D^2-d^2)$

$\therefore$ Work done $=$ surface tension $\times$ change in area

$=2\pi S(D^2-d^2)$