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 :

Solution

Physics sir · 3 steps

Check each statement on its own: contact angle depends on the pair, capillary rise depends on the radius.

1. Statement I. The contact angle θ is set by how strongly the liquid molecules attract each other (cohesion) compared with how strongly they attract the solid (adhesion). Both forces depend on the materials, so θ depends on the solid and the liquid together. Water on clean glass gives nearly 0°, while mercury on glass gives about 140°. Statement I is true.

   h = (2T cos θ)/(rρ g)

2. Statement II. In this formula for capillary rise, the inner radius r sits in the denominator, so h ∝ 1/r. Halve the radius and the liquid rises twice as high. Statement II is false.
3. So. Statement I is true and Statement II is false, which is option (d).

The idea to keep. Contact angle belongs to a solid and liquid pair, never to one material alone. Capillary rise follows h = (2T cos θ)/(rρ g), so a narrower tube always means a higher rise.

Answer from the NTA final answer key. Solution by PrepWiser.