Question

One drop of soap bubble of diameter $D$ breaks into $27$ drops having surface tension $\sigma$. The change in surface energy is

• A. $2\pi \sigma D^2$
• B. $4\pi \sigma D^2$
• C. $\pi \sigma D^2$
• D. $8\pi \sigma D^2$

Answer 1

The correct option is D $8\pi \sigma D^2$

Volume of bigger bubble = volume of $27$ smaller bubbles

$\Rightarrow \frac{4}{3}\pi D^3=27\times \frac{4}{3}\pi d^3\Rightarrow d=\frac{D}{3}$

Initial surface energy $S_i=4\pi D^2\sigma$

Final surface energy $S_f=27\times 4\pi d^2\sigma$

$\Delta S=S_f-S_i$ and using $d=\frac{D}{3}$

$\Delta S=\sigma \times 4\pi [27\times \frac{D^2}{9}-D^2]$

$=2D^2\times 4\pi \times \sigma =8\pi \sigma D^2$