Q. Two very wide parallel glass plates are held vertically at a small separation $r$, and dipped in water of surface tension $S$. Some water climbs up in the gap between the plates. If $p_{0}$ is the atmospheric pressure, then the pressure of water just below the water surface in the region between the two plates is
A) $p_{0} - \frac{2\ S}{r}$
B) $p_{0} + \frac{2\ S}{r}$
C) $p_{0} - \frac{4\ S}{r}$
D) $p_{0} + \frac{4\ S}{r}$
Explanation
(a) Here, the free liquid surface between the plates will be cylindrical which is curved along one axis (parallel to the plates). The radius of curvature of meniscus,$\ R = r/2$. For cylindrical surface
$p_{0} - p = \frac{S}{R} = \frac{S}{r/2} = \frac{2S}{r}$
$\therefore p = p_{0} - \frac{2S}{r}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.