Question

If the excess pressure inside a soap bubble is three times that of other bubble, then the ratio of their volumes will be

• A. $1:3$
• B. $1:10$
• C. $1:17$
• D. $1:27$

Answer 1

Answer: (D)

$1:27$

The excess pressure inside a soap bubble,
$△p=\frac{4T}{r}$
i.e., $△p\propto \frac{1}{r}$
$\frac{△p_1}{p_2}=\frac{r_2}{r_1}=\frac{3}{1}$
Hence, $\frac{V_1}{V_2}={\left(\frac{r_1}{r_2}\right)}^3={\left(\frac{1}{3}\right)}^3=\frac{1}{27}$.