MCQ
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$1: 81$
- ✓$1: 27$
✓
Answer
Correct option: D.
$1: 27$
d
$\mathrm{P}_1-\mathrm{P}_0=\frac{4 \mathrm{~T}}{\mathrm{r}_1} \quad \mathrm{P}_2-\mathrm{P}_0=\frac{4 \mathrm{~T}}{\mathrm{r}_2}$
$\mathrm{P}_1-\mathrm{P}_0=\frac{4 \mathrm{~T}}{\mathrm{r}_1} \quad \mathrm{P}_2-\mathrm{P}_0=\frac{4 \mathrm{~T}}{\mathrm{r}_2}$
$\mathrm{P}_1-\mathrm{P}_0=3\left(\mathrm{P}_2-\mathrm{P}_0\right)$
$\frac{4 \mathrm{~T}}{\mathrm{r}_1}=3 \frac{4 \mathrm{~T}}{\mathrm{r}_2}$
$\mathrm{r}_2=3 \mathrm{r}_1$
$\frac{\mathrm{V}_1}{\mathrm{~V}_2}=\frac{\frac{4}{3} \pi \mathrm{r}_1^3}{\frac{4}{3} \pi \mathrm{r}_2^3}=\frac{1}{27}$
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