JEE Advanced · Physics · 11. Properties of Fluids

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $σ$ . The angle of contact between water and the wall of the capillary tube is $θ$ . Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

A For a given material of the capillary tube, $h$ decreases with increase in $r$
B For a given material of the capillary tube, $h$ is independent of $σ$
C If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases
D $h$ is proportional to contact angle $θ$

Verified Solution

Answer & Solution

Correct Answer

(C) If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases

Step-by-step Solution

Detailed explanation

\frac{2 σ}{R} = ρ g h

[R \to R a d i u s o f m e n i s c u s]

h = \frac{2 σ}{R ρ g}

R = \frac{r}{\cos θ}

[r→radius of capillary;

θ \to

contact angle]

h = \frac{2 σ \cos θ}{r ρ g}

(A)

For given material,

θ = c o n s t a n t

h \propto \frac{1}{r}

(B)

h depends on

σ

(C)

If lift is going up with constant acceleration,

g_{e f f} = (g + a)

h = \frac{2 σ \cos θ}{r ρ (g + a)}

It means h decreases

(D)

h is proportional to

\cos θ, N o t θ

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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