Q.
Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is $\rho$, the surface tension of water is $T$ and the atmospheric pressure is $P_{0}$. Consider a vertical section $ABCD$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude
A) $|2P_{0}Rh + \pi R^{2}\rho gh - 2RT|$
B) $|2P_{0}Rh + R\rho gh^{2} - 2RT|$
C) $|P_{0}\pi R^{2} + R\rho gh^{2} - 2RT|$
D) $|P_{0}\pi R^{2} + R\rho gh^{2} + 2RT|$
Explanation
(b) Net force = Average pressure $\times$ Area – T $\times$ 2R
$\left( P_{0} + \rho g\frac{h}{2} \right)(2Rh) - T2R$
$\Rightarrow |2P_{0}Rh + R\rho gh^{2} - 2RT|$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.