Question
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?

h = r

h > r

h < r

None of these
medium
Solution
h = r
Consider a cylindrical vessel of radius r filled with a liquid of density to a height h. If p_{0} 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 p_{0}, 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 F_{B} = F_{C}; so from eq. (i) and (ii),
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