MCQ
The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is ($T=$ surface tension of the solution)
- A$4\pi ({D^2} - {d^2})T$
- B$8\pi ({D^2} - {d^2})T$
- C$\pi ({D^2} - {d^2})T$
- ✓$2\pi ({D^2} - {d^2})T$
✓
Answer
Correct option: D.
$2\pi ({D^2} - {d^2})T$
d
(d)$W = T \times 8\pi (r_2^2 - r_1^2) = T \times 8\pi \left( {\frac{{{D^2}}}{4} - \frac{{{d^2}}}{4}} \right)$
$ = 2\pi ({D^2} - {d^2})T$
(d)$W = T \times 8\pi (r_2^2 - r_1^2) = T \times 8\pi \left( {\frac{{{D^2}}}{4} - \frac{{{d^2}}}{4}} \right)$
$ = 2\pi ({D^2} - {d^2})T$
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