Question

What is the relation obeyed by the angles of contact $ \theta_1 $, $ \theta_2 $ and $ \theta_3 $ of 3 liquids of different densities $ P_1 $, $ P_2 $, and $ P_3 $ respectively $ (P_1<P_2<P_3) $ when they rise to the same capillary height in 3 identical capillaries and having nearly the same surface tension $ T $?

• A. \( 0<\theta_3<\theta_2<\theta_1<\frac{\pi}{2} \)
• B. \( \frac{\pi}{2}>\theta_1>\theta_2>\theta_3>0 \)
• C. \( \frac{\pi}{2}>\theta_1>\theta_2>\theta_3<\frac{\pi}{2} \)
• D. \( 0<\theta_1<\theta_2<\theta_3<\frac{\pi}{2} \)

Hint:

In capillary action, the angle of contact decreases with the increase in liquid density. This relationship can be used to predict the rise of liquids in capillaries.

Answer 1

The Correct Option is A

When a liquid rises in a capillary tube, the height of the rise is inversely proportional to the density of the liquid and directly proportional to the surface tension. 
The angle of contact (\( \theta \)) of the liquid with the capillary wall is also related to the density of the liquid. For a liquid with higher density, the angle of contact tends to be greater. In this case, we have three liquids with densities \( P_1 \), \( P_2 \), and \( P_3 \) such that \( P_1<P_2<P_3 \). According to the relationship between the angle of contact and density: - The liquid with the lowest density (\( P_1 \)) will have the highest angle of contact. - The liquid with the highest density (\( P_3 \)) will have the smallest angle of contact. 
Therefore, the relation between the angles of contact is: \[ 0<\theta_3<\theta_2<\theta_1<\frac{\pi}{2} \] 
Thus, the correct answer is option A.