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?

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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?

diffcult

Solution

Correct option is

h = r

Let a cylindrical with radius of cross-section 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,

p₂ = 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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