Q. To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid presses on the sides of the vessel equal to the force exerted by the liquid on the bottom of the vessel. If should be
A) Equal to the radius
B) Less than radius
C) More than radius
D) Four times of radius
Explanation
(a) Let $h$ be the desired height of liquid in cylinder for which the force on the bottom and sides of the vessel is equal
Force on bottom $= \rho\ gh \times \pi R^{2}$
Force on the walls of vessel
$= \rho\ g\ (h/2) \times 2\pi R\ h$
$= \rho\ g\ \pi h^{2}R = \rho\ g\ h\ \pi\ Rh$ or $R = h$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.