Question

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

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

Answer 1

Answer: (C)

$1:27$

Given :- Pressure in bubble $1=3\times Pressureinbubble2$

$P_1=3P_2$

& we know that Pressure $\propto \frac{1}{radiusofbubble}$

Hence,

$\frac{P_1}{P_2}=\frac{r_2}{r_1}=3$

So $\frac{r_1}{r_2}=\frac{1}{3}$

& Volume = $\frac{4}{3}\Pi r^3$

Hence $\frac{v_1}{v_2}={\left(\frac{r_1}{r_2}\right)}^3=\frac{1}{27}$