Question

The excess pressure inside a soap bubble is three times than excess pressure inside a second soap bubble, then the ratio of their surface area is

• A. $9 : 1$
• B. $1 : 3$
• C. $1 : 9$
• D. $3 : 1$

Answer 1

Answer: (C)

$1 : 9$

Answer 2

Pressure, $P=\frac{4S}{r}$ or $P \propto\frac{1}{r}$ $\therefore \frac{P_{1}}{P_{2}}=\frac{r_{2}}{r_{1}}=\frac{3}{1} \ldots\left(i\right)$ or $r_{2}=3r_{1}$ Also $\frac{A_{1}}{A_{2}}=\frac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{2} =\left(\frac{r_{1}}{3r_{1}}\right)^{2} \left(Using \left(i\right)\right)$ $=\frac{1}{9}$