Question

The excess pressure inside one soap bubble is three times that inside a second soap bubble. The ratio of the volumes of the two bubbles is

• A. $1:9$
• B. $9:1$
• C. $1:27$
• D. $27:1$

Answer 1

The correct option is C $1:27$

Since we know that Pressure inside a bubble is universely proportional to radius, i.e.,

$\frac{P_1}{P_2}=\frac{r_2}{r_1}=3\left(given\right)\Rightarrow \frac{r_1}{r_2}=\frac{1}{3}$

& Volume $\propto$ ${\left(Radius\right)}^3\Rightarrow \frac{V_1}{V_2}={\left(\frac{r_1}{r_2}\right)}^3=\frac{1}{27}$