To What Height Should A Cylindrical Vessel Be Filled With A Homogeneous Liquid To Make The Force With Which The Liquid Passes On The Side Of The Vessel Equal To The Force Exerted Be The Liquid On The Bottom Of The Vessel?

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To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid passes on the side of the vessel equal to the force exerted be the liquid on the bottom of the vessel?


Correct option is

h = r

Consider a cylindrical vessel of radius r filled with a liquid of density  to a height h. If p0 is the atmospheric pressure, the pressure difference inside and outside the base of the cylinder,



Now as pressure at a depth y below the surface of liquid inside will be  while outside p0, so pressure difference on two sides of the curved surface at depth 0 below the surface will be 


So the force on a strip of curved surface of thickness dy at depth below the surface of the liquid as show in figure will be



But according to given problem FB = FC; so from eq. (i) and (ii),  




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