Question 104 of 192

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

A$1: 9$B$1: 3$C$1: 27$D$1: 81$

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Answer: (C) $1: 27$

$\mathrm{P}_1-\mathrm{P}_0=\frac{4 \mathrm{~T}}{\mathrm{r}_1} \qquad \quad \quad \quad\mathrm{P}_2-\mathrm{P}_0=\frac{4 \mathrm{~T}}{\mathrm{r}_2}$
$\begin{aligned} & \mathrm{P}_1-\mathrm{P}_0=3\left(\mathrm{P}_2-\mathrm{P}_0\right) \\ & \frac{4 \mathrm{~T}}{\mathrm{r}_1}=3 \frac{4 \mathrm{~T}}{\mathrm{r}_2} \\ & \mathrm{r}_2=3 \mathrm{r}_1 \\ & \frac{\mathrm{V}_1}{\mathrm{~V}_2}=\frac{\frac{4}{3} \pi \mathrm{r}_1^3}{\frac{4}{3} \pi \mathrm{r}_2^3}=\frac{1}{27}\end{aligned}$

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