Question

Two liquids A and B have $\theta_{\mathrm{A}}$ and $\theta_{\mathrm{B}}$ as contact angles in a capillary tube. If $K=\cos \theta_{\mathrm{A}} / \cos \theta_{\mathrm{B}}$, then identify the correct statement:

• A. K is negative, then liquid A and liquid B have convex meniscus.
• B. K is negative, then liquid A and liquid B have concave meniscus.
• C. K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.
• D. K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.

Hint:

The sign of $K$ indicates the nature of the meniscus of the liquids.

Answer 1

The Correct Option is C

1. Given: \[ K = \frac{\cos \theta_{\mathrm{A}}}{\cos \theta_{\mathrm{B}}} \] 
2. Interpretation: 
- If $K$ is negative, $\cos \theta_{\mathrm{A}}$ and $\cos \theta_{\mathrm{B}}$ are of opposite signs. 
- This implies that one liquid has a concave meniscus and the other has a convex meniscus. 
Therefore, the correct answer is (3) K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.