Question

Two soap bubbles of radius $R_{1}$ and $R_{2}$ coalesce isothermally in vacuum to form a single soap bubble. The radius of the bigger bubble formed is

• A. $\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$
• B. $\frac{1}{R}=\frac{1}{R_{1}}-\frac{1}{R_{2}}$
• C. $\sqrt{R_{1}^{2} + R_{2}^{2}}$
• D. $\frac{1}{R}=\frac{1}{R_{1}^{2}}+\frac{1}{R_{2}^{2}}$

Answer 1

Answer: (C)

$P_{1}V_{1}+P_{2}V_{2}=PV$ (no. of moles constant)
$\frac{4 T}{R_{1}}\cdot \frac{4}{3}\pi R_{1}^{3}+\frac{4 T}{R_{2}}\cdot \frac{4}{3}\pi R_{2}^{3}=\frac{4 T}{R}\frac{4}{3}\pi R^{3}$
$R=\sqrt{R_{1}^{2} + R_{2}^{2}}$