Question

Water rises to a height $h$ in a capillary tube lowered vertically into the water to a depth $l$ as shown in the figure. The lower end of the tube is now closed, the tube is then taken out of the water and opened again. The length of the water column remaining in the tube will be:

• A. $2h$ if $l\ge h$ and $l+h\le h$
• B. $h$ if $l\ge h$ and$l+h$ if $l\le h$
• C. $4h$ if $l\ge h$ and $l-h$ if $l\le h$
• D. $\frac{h}{2}$ if $l\ge h$ and $l+h$ if $l\le h$

Answer 1

The correct option is A $2h$ if $l\ge h$ and $l+h\le h$

$Case1:$ The force of surface tension supports the weight of column $h$ of water. When the tube is taken out of the water and opened, a convex meniscus is formed at the lower end. The force of surface tension around this meniscus balances another column $h$ of water. Hence, total length of water column remaining in the tube $h+h=2h$ if $l>h$.

$Case2:$ If $l<h$, the force of surface tension around lower meniscus is capable of balancing the column $l$ of liquid. Hence, length of water remaining in the tube $=l+h$