Question

Three liquids have same surface tension and densities \(ρ_1\), \(ρ_2\) and \(ρ_3\) (\(ρ_1 < ρ_2 < ρ_3\)). In three identical capillaries rise of liquid is same. The corresponding angle of contact \(θ_1\), \(θ_2\) and \(θ_3\) are related as

• A. \(θ_1 < θ_2 < θ_3\)
• B. \(θ_1 > θ_2 > θ_3\)
• C. \(θ_1 = θ_2 = θ_3\)
• D. \(θ_1 > θ_2 < θ_3\)

Hint:

Capillary rise h = 2T cos(theta) / (r rho g), so cos(theta) is proportional to density when h, T, r are fixed.

Answer 1

The Correct Option is B

Step 1: Same rise
From the formula $h \propto \cos\theta/\rho$ at fixed $T$ and $r$, so equal rise means $\cos\theta/\rho$ is constant.

Step 2: Order
So $\cos\theta$ grows with $\rho$: $\cos\theta_1 < \cos\theta_2 < \cos\theta_3$.

Step 3: Angles
The smaller the cosine, the larger the angle, so $\theta_1 > \theta_2 > \theta_3$. Option (B).

Final Answer:
Option (B). \[ \boxed{\theta_1 > \theta_2 > \theta_3} \]