Question

Water rises to height $h$ in the capillary tube. If the length of the capillary tube above the surface of the water is made less than $h$ then:

• A. Water does not rise at all.
• B. Water rises up to a point a little below the top and stays there.
• C. Water rises up to the tip of the capillary tube and then starts overflowing like a fountain.
• D. Water rises up to the top of the capillary tube and stays there without overflowing.

Answer 1

The correct option is D

Water rises up to the top of the capillary tube and stays there without overflowing.

Explanation for correct option:

• Consider a beaker filled with some liquid, dip a capillary tube into it. The liquid in the capillary tube will rise (as compared to the surface of liquid in beaker)

• Let $R$ be the radius of tube or radius of meniscus, $\sigma$ be the surface tension, and $\rho$ be the density of the liquid.
• Now, the height ($h$) up to which a liquid rises is given as $h=\frac{2\sigma }{\rho gR}$
• Here, $g$ is the acceleration due to gravity.
• Also notice that the term $\frac{2\sigma }{\rho g}$ is constant, therefore $R\propto \frac{1}{h}$
• Now when height is reduced then the radius of the meniscus increases.
• Thus, the liquid reaches the top of capillary tube, and it doesn't overflow.
• Therefore, water rises up to the top of capillary tube and stays there without overflowing.

Hence, the correct option is (D).

Explanation for incorrect option:

• The liquid won't overflow because by doing so, it will create constant flow, constant energy, but without any energy input.
• The same force that pulls the water along inside the capillary tube also holds it there when it reaches the end.
• This force does not pull upward, it will pull the water along the glass.
• At certain water the weight of water balances this pull and it would not overflow.

Hence, option (A), (B), and (C) are incorrect.