Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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

water rises upto the tip of capillary tube and then starts overflowing like a fountain

water rises upto the top of capillary tube and stays there without overflowing

water rises upto a point a little below the top and stays there

water does not rise at all

Capillary Rise Formula: The height $h$ to which a liquid rises is given by $h = \frac{2T \cos \theta}{r \rho g}$ , where $T$ is surface tension, $\theta$ is the angle of contact, $r$ is the tube radius, and $\rho$ is density .
Insufficient Length: If the length of the tube $L$ is less than the calculated height $h$ ( $L < h$ ), the liquid will rise to the top of the tube.
Adjustment of Meniscus: Upon reaching the top, the liquid does not overflow. Instead, the meniscus changes its shape. The radius of curvature of the meniscus ( $R$ ) increases (making the meniscus flatter), which effectively changes the contact angle $\theta$ to a new value $\theta'$ .
New Equilibrium: The new condition for equilibrium becomes $L = \frac{2T \cos \theta'}{r \rho g}$ . Since $L < h$ , it follows that $\cos \theta' < \cos \theta$ , meaning the contact angle increases. The liquid stays at the brim in equilibrium.

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