Question

The excess pressure inside the first soap bubble is three times that inside the second soap bubble. The ratio of the volume of the first soap bubble to the volume of the second soap bubble is

• A. \(3:4\)
• B. \(1:3\)
• C. \(1:9\)
• D. \(1:27\)

Hint:

Capillary rise is 2T cos(theta) divided by r rho g; with equal rise, cos(theta) is proportional to density.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Capillary rise: \(h = \frac{2T\cos\theta}{r\rho g}\). Here T, r, g and h are the same for all three liquids.

Step 2: Relate theta and density:
Equal h means \(\frac{\cos\theta}{\rho}\) is constant, that is, \(\cos\theta\propto\rho\).

Step 3: Order the angles:
Since \(\rho_1 < \rho_2 < \rho_3\), we have \(\cos\theta_1 < \cos\theta_2 < \cos\theta_3\). Cosine decreases as the angle increases in \(0\) to \(90^\circ\), so \(\theta_1 > \theta_2 > \theta_3\).

Final Answer:
The angles of contact satisfy \(\theta_1 > \theta_2 > \theta_3\), option (B). \[ \boxed{\theta_1 > \theta_2 > \theta_3} \]