Question

Two soap bubbles, A and B, have radii in the ratio \(3:2\). The excess pressure inside the bubble A to that of B is in the ratio

• A. \(2:3\)
• B. \(3:2\)
• C. \(1:5\)
• D. \(4:9\)

Hint:

Excess pressure inside a soap bubble is 4T/R, so radius is inversely proportional to pressure.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A soap bubble has two surfaces, so the excess pressure is \(\Delta P = \frac{4T}{R}\), giving \(R\propto\frac{1}{\Delta P}\).

Step 2: Radius ratio:
\(\Delta P_1 = 3\Delta P_2\), so \(\frac{R_1}{R_2} = \frac{\Delta P_2}{\Delta P_1} = \frac13\).

Step 3: Volume ratio:
Volume \(\propto R^3\), so \(\frac{V_1}{V_2} = \left(\frac13\right)^3 = \frac{1}{27}\). So the ratio is \(1:27\).

Final Answer:
The ratio of volumes is \(1:27\), option (A). \[ \boxed{1:27} \]