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?

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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