Question

The excess pressure inside one soap bubble is three times that inside a second soap bubble, then the ratio of their surface areas is:

• A. $1:9$
• B. $1:3$
• C. $3:1$
• D. $1:27$

Answer 1

The correct option is A $1:9$

$\frac{\Delta P_1}{\Delta P_2}=\frac{\frac{4T}{R_1}}{\frac{4T}{R_2}}=\frac{R_2}{R_1}=3$
Also,
$\frac{A_1}{A_2}=\frac{4\pi R_1^2}{4\pi R_2^2}={\left(\frac{R_1}{R_2}\right)}^2={\left(\frac{1}{3}\right)}^2$
$\Rightarrow \frac{A_1}{A_2}=\frac{1}{9}$