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Given below are two statements: Statement-I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement-II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below:

Asked in JEE Main 4th April 2nd Shift 2024 · Concept and assertion

• (1) Both Statement-I and Statement-II are false.
• (2) Statement-I is true but Statement-II is false.
• (3) Statement-I is false but Statement-II is true.
• (4) Both Statement-I and Statement-II are true.

Step-by-step solution

Why the other options are wrong

• (1) comes from calls Statement-I false as well; the contact angle follows from cos θ=(T_sg-Tₛₗ)/(T_lg), in which the solid and the liquid both appear, so it is a property of the pair.
• (3) comes from rejects Statement-I and accepts Statement-II, the wrong way round on both; the contact angle is fixed by the solid-liquid, solid-gas and liquid-gas tensions together, and the capillary rise carries r in its denominator.
• (4) comes from accepts Statement-II; h=(2T cos θ)/(ρ gr) makes the rise inversely proportional to the radius, which is why a fine tube lifts water far higher than a wide one.

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