Question

The excess of pressure inside the first soap bubble is two tines that inside the second bubble The ratio of radii of the first to that of the second bubble is

• A. 1 :4
• B. 1 :2
• C. 1 :8
• D. 4 :1

Answer 1

The correct option is C 1 :8

$P_1=\frac{4T}{r_1}$

$P_2=\frac{4T}{r_2}$

$\frac{P_1}{P_2}=\frac{r_2}{r_1}$

$\frac{r_2}{r_1}=3$

$\frac{r_2}{r_1}=2$

$r_2=2r_1$

$\frac{V_1}{V_2}=\frac{\frac{4\pi }{3}{r_1}^3}{\frac{4\pi }{3}{r_2}^3}$

$={\left(\frac{r_1}{r_2}\right)}^3$

$={\left(\frac{1}{2}\right)}^3$

$=\frac{1}{8}$

Hence,

option $\left(C\right)$ is correct answer.