Question

Figure shows a capillary tube of radius $r$ dipped into water. The atmospheric pressure is $P_0$ and the capillary rise of water is $h$. $s$ is the surface tension for water-glass.


The pressure inside water at the point $A$ (lowest point of the meniscus) is

• A. $P_0$
• B. $P_0-\frac{2s}{r}$
• C. $P_0-\frac{4s}{r}$
• D. $P_0+\frac{2s}{r}$

Answer 1

The correct option is B $P_0-\frac{2s}{r}$

Left diagram is the front view and the right diagram is the top view of the meniscus
Due to atmospheric pressure, a force is acting downward i.e. $F_{P_0}=P_0\pi r^2$
Due to surface tension a force is acting upward i.e. $F_s=s\times 2\pi r$
There is one more pressure that is pressure inside that surface that is also in the upward direction and the force due to this pressure is $F_A=P_A\times \pi r^2$


On equating these forces,
$F_{P_0}=F_A+F_s$

$P_0\pi r^2=P_A\times \pi r^2+s\times 2\pi r$
$P_{0}r=P_{A}r+2s$
$P_A=P_0-\frac{2s}{r}$