JEE Main 2025 · 4 April · morning · Single correct · +4 / −1
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 zero, then liquid A has convex meniscus and liquid B has concave meniscus.
- (d) K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.
Answer and solution
Answer (d) K is negative, then liquid A has concave meniscus and liquid B has convex…
Solution
Physics sir · 3 steps
Sign of cos θ fixes the meniscus, so a negative K means the liquids curve opposite ways.
- Angle sets shape. If θ < 90°, then cos θ > 0 and the liquid wets the glass, giving a concave meniscus. If θ > 90°, then cos θ < 0 and the meniscus is convex. If θ = 90°, then cos θ = 0 and the surface is flat.
Sign of K What it means Meniscus of A and B K > 0 cos θ_A and cos θ_B have the same sign both concave or both convex K < 0 cos θ_A and cos θ_B have opposite signs one concave, one convex K = 0 cos θ_A = 0, so θ_A = 90° A is flat, B is not fixed by K - Check the options. A negative K rules out (a) and (b), because both of those give the two menisci the same shape. A zero K makes A flat, not convex, so (c) fails. Option (d) gives A concave (cos θ_A > 0) and B convex (cos θ_B < 0), which makes K negative.
- So. Only (d) is consistent: when K is negative, one liquid is concave and the other is convex, and (d) describes that case.
The idea to keep. Acute contact angle means positive cosine and a concave meniscus. Obtuse means negative cosine and a convex meniscus. A ratio of cosines is negative only when the two liquids curve opposite ways.
Answer from the NTA final answer key. Solution by PrepWiser.