Given below are two statements :
Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be 0°.
Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
In the light of the above statement, choose the correct answer from the options given below.

Solution

Physics sir · 4 steps

No rise and no fall means h = 0, so cos θ = 0 and θ = 90°, not 0°.

1. Capillary rise formula. The height a liquid climbs in a tube of radius r depends on the contact angle θ through cos θ.

   h = (2T cos θ)/(rρ g)

2. Check Statement I. For h = 0 you need cos θ = 0, so θ = 90°. At θ = 0°, cos θ = 1 is at its largest, so the rise is the greatest, not zero. Statement I is false.
3. Check Statement II. The contact angle comes from the balance between the liquid's cohesion and its adhesion to the solid. Change either the solid or the liquid and the angle changes, so it is a property of the pair. Statement II is true.
4. So. Statement I is false and Statement II is true, which is option (b).

The idea to keep. Capillarity hinges on cos θ: below 90° the liquid rises, at 90° it stays level, above 90° it falls. And θ belongs to the solid and liquid pair.

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