A cylindrical vessel is filled with a liquid of density `rho` to a height h such that the force exerted by the liquid on the bottom is equal to the force exerted on the walls of the vessel. Then h should be

Options

A. equal to radius
B. more than the radius
C. less than the radius
D. two times the radius

Answer

A

Explanation

Force exerted by the liquid on the bottom
`F_(1)=` pressure `xx` area `=rhoghxxpir^(2)`
The force exerted on the walls of the vessel.
`F_(2)=rhog((h)/(2))xx2pirxxh` [Mean pressure on the walls of the beaker is `(hrhog)/(2)`]
But `F_(1)=F_(2)impliesrhoghpir^(2)=rhogh^(2)pir :.h=r`