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

(C) K is negative, then liquid A has concave meniscus and liquid B has convex meniscus

(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.

(D) K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Fluid Mechanics

Two liquids A and B have

θ_{A}

and

θ_{B}

as contact angles in a capillary tube. If

K = cos θ_{A} / cos θ_{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✓ Correct
(D)K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.

Answer: (C)

The ratio

K = cos θ_{A} / cos θ_{B}

is negative only when the two cosines carry opposite signs. A liquid that wets the tube has a contact angle below

9 0^{\circ}

(positive cosine) and forms a concave meniscus, while a non-wetting liquid has a contact angle above

9 0^{\circ}

(negative cosine) and forms a convex meniscus. A negative

K

therefore means one liquid is concave and the other convex; with

cos θ_{A}

positive and

cos θ_{B}

negative, liquid A has a concave meniscus and liquid B a convex meniscus.

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Single correct option