Water rises to a height $h$ in a capillary tube. If the length of the capillary tube above the surface of wate

Question

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:

Accepted Answer

1. **Capillary Rise Formula:** The height $h$ to which a liquid rises is given by $h = \frac{2T \cos 	heta}{r ho g}$, where $T$ is surface tension, $	heta$ is the angle of contact, $r$ is the tube radius, and $ho$ is density .
2. **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.
3. **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 $	heta$ to a new value $	heta'$.
4. **New Equilibrium:** The new condition for equilibrium becomes $L = \frac{2T \cos 	heta'}{r ho g}$. Since $L < h$, it follows that $\cos 	heta' < \cos 	heta$, meaning the contact angle increases. The liquid stays at the brim in equilibrium.

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