Question

Pressure inside two soap bubbles are $1.06$ and $1.08$ atm. Ratio between their volumes is

• A. $16:25$
• B. $64:27$
• C. $16:9$
• D. $3:10$

Answer 1

Answer: (B)

Excess pressures $\left(\Delta P_1\right)P_i-P_0=1.06-1=0.06$ atm
$\left(\Delta P_2\right)P_i-P_0=1.08-1=0.08$ atm
$\Delta P=\frac{4S}{R}$
$\Rightarrow R=\frac{4S}{\Delta P}$
$\Rightarrow \frac{R_1}{R_2}=\frac{\Delta P_2}{\Delta P_1}$
$\frac{R_1}{R_2}=\frac{0.08}{0.06}=\frac{8}{6}=\frac{4}{3}$
$\therefore \frac{V_1}{V_2}={\left(\frac{R_1}{R_2}\right)}^3={\left(\frac{4}{3}\right)}^3=\frac{64}{27}$