Question 5

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:

Excess pressure inside a soap bubble: $$P = \frac{4T}{r}$$, where $$T$$ is surface tension and $$r$$ is radius.

Given $$P_1 = 3P_2$$: $$\frac{4T}{r_1} = 3 \cdot \frac{4T}{r_2} \implies r_2 = 3r_1$$.

Volume ratio: $$\frac{V_1}{V_2} = \frac{r_1^3}{r_2^3} = \frac{r_1^3}{27r_1^3} = \frac{1}{27}$$.

The correct answer is Option 3: $$1:27$$.

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