Question

Two soap bubbles are blown. In first bubble, excess pressure is $4$ times that of second bubble. The ratio of the radii of first and second soap bubble is

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

Answer 1

The correct option is B $1:4$

We know,
Excess pressure, $\Delta P=\frac{4T}{R}$
Excess pressure in bubble 1, $\Delta P_1=\frac{4T}{R_1}$
Excess pressure in bubble 2, $\Delta P_2=\frac{4T}{R_2}$
$\therefore \frac{\Delta P_1}{\Delta P_2}=\frac{\frac{4T}{R_1}}{\frac{4T}{R_2}}=\frac{R_2}{R_1}=4$
$\therefore R_2=4R_1$
$\therefore \frac{R_1}{R_2}=\frac{1}{4}$