Question
A cylindrical jar has radius r. To what height h should it be filled with a liquid so that the force exerted by the liquid on the sides of the jar equals the force exerted on the bottom?

h = r

h = 2r

h = 4r

None of these

diffcult
Solution
h = r
Let a cylindrical with radius of crosssection r be filled with a homogeneous liquid of density up to a height h.
Pressure at the bottom of the cylinder,
Pressure at the top of the liquid surface,
p_{2} = 0
Average pressure on the sides of the cylinder,
Force on the sides of the vessel = average pressure area
Force on the bottom of the vessel,
Two forces will be equal if
or h = r.
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