Question
The excess pressure inside a soap bubble is thrice the excess pressure inside a moving soap bubble. What is the ratio between the volume of the first and second bubble?
✓
Answer
Let $r_1$ and $r_2$ be the radii of soap bubbles, excess pressure in them are $\frac{4\sigma}{\text{r}_1}$ and $\frac{4\sigma}{\text{r}_2},$ where $\sigma$ is the surface tension. Given: $\text{P}_1=\text{3P}_2$$\frac{4\sigma}{\text{r}_1}=3\frac{4\sigma}{\text{r}_2}$
$\therefore\text{r}_2=3\text{r}_1$
Volume fo first to second bubble,$=\frac{\text{r}_1^3}{\text{r}^3_2}=\frac{1}{3^3}=\frac{1}{27}$
$\therefore\text{r}_2=3\text{r}_1$
Volume fo first to second bubble,$=\frac{\text{r}_1^3}{\text{r}^3_2}=\frac{1}{3^3}=\frac{1}{27}$
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