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Question

# To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid pressure on the sides of the vessel equal to the force exerted by the liquid on the bottom of the vessel?

A
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C
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Solution

## The correct option is B Equal to the radius.If h is the height of liquid in cylinder, r be the radius of the cylinder and ρ be the density of the liquid.Then we haveWeight of the liquid =πr2hρg........................................(I)Mean pressure on the wall =12ρghThe total force on the wall = 2πrh×12ρgh=πrh2ρg....................................(2)On equating (I) and (2) we haveπr2hρg=πrh2ρgr=h∴ The liquid should be filled up-to a height equal to the radius of the cylinder.

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