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: Rearrange the formula:
$\cos\theta = \frac{h\,r\,\rho\,g}{2T}$. Everything except $\rho$ is common.

Step 2: Compare:
A denser liquid gives a larger $\cos\theta$, hence a smaller angle. The densest, liquid 3, has the smallest angle and the lightest, liquid 1, has the largest. So $\theta_1 > \theta_2 > \theta_3$ (B).

Final Answer:
$\theta_1 > \theta_2 > \theta_3$. \[ \boxed{\theta_1 > \theta_2 > \theta_3} \]