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 :

Statement I is true but Statement II is false.

Both Statement I and Statement II are false.

Both Statement I and Statement II are true.

Statement I is false but Statement II is true.

Properties of Matter PYQ — JEE Main 2024 · 4 Apr · Shift 2 · Q77 with Solution

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Correct answer: D

Analyze Statement I

The contact angle $\theta$ depends on the nature of:
- the liquid,
- the solid surface,
- and also the surrounding medium.
From Young’s equation,
$T_{SA} = T_{SL} + T_{LA}\cos\theta$
where the interfacial tensions depend on the materials involved.

Hence, the contact angle is indeed a property of the pair solid-liquid materials.

So, Statement I is true.
Analyze Statement II

The capillary rise is given by
$h = \frac{2T\cos\theta}{\rho g r}$
where
- $T$ = surface tension,
- $\theta$ = contact angle,
- $\rho$ = density of liquid,
- $r$ = inner radius of the capillary tube.
From the formula,
$h \propto \frac{1}{r}$
So the rise of liquid does depend on the inner radius of the tube.

Therefore, Statement II is false.
Choose the correct option
- Statement I: True
- Statement II: False
Therefore, the correct option is:
$\boxed{\text{D}}$
Comparison with stored answer

Stored correct answer = D

My derived answer = D

They match.