Question

A capillary tube is dipped in water up to length l, the level of water reaches up to height h. Now the end which is inside the water is closed and the capillary tube is put out side the water and that closed end is opened if l > h, the height of the remaining water column in the capillary will be:

• A. 0
• B. l + h
• C. 2h
• D. h

Answer 1

The correct option is C 2h

Liquid rises to height $h$, which can be obtained by ascent formula as
$h=\frac{2T}{r\rho g}$ .... $\left(I\right)$
When the tube is taken out, liquid weight is balanced by upward surface tension forces.
$\Rightarrow W=2\pi rT+2\pi rT=4\pi rT$ (considering surface tension forces at both A and B )
$\Rightarrow \left(\pi r^{2}H\right)\rho g=4\pi rT\Rightarrow H=\frac{4T}{r\rho g}$ .... $\left(II\right)$
from $\left(I\right)$ and $\left(II\right)$, we have
$H=2h$