Question

Two soap bubbles of radii $r$ and $2r$ are connected by a capillary tube-valve arrangement shown in the diagram. The valve is now opened. Then which one of the following will result?

• A. The radii of the bubbles will remain unchanged.
• B. The bubbles will have equal radii.
• C. The radius of the smaller bubble will increase and that of the bigger bubble will decrease.
• D. The radius of the smaller bubble will decrease and that of the bigger bubble will increase.

Answer 1

The correct option is D The radius of the smaller bubble will decrease and that of the bigger bubble will increase.

Pressure difference $=\frac{4T}{R}$
For smaller soap, $p_{atm}-p_{i1}=\frac{4T}{r}$
For bigger soap,$p_{atm}-p_{i2}=\frac{4T}{2r}$
As pressure inside smaller bubble is greater than pressure inside the bigger bubble, so air flows from smaller to bigger and thus radius of the smaller bubble will decrease and that of the bigger bubble will increase.