To what height should a cyclindrical 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 ?

Options

A. Half of the radius of the vessel
B. Radius of the vessel
C. One-fourth of the radius of the vessel
D. Three-fourth of the radius of the vessel

Answer

B

Explanation

Pressure at the bottom= `h rho g`
Pressure in the vertical surface=`1/2 rho gh`
`implies F_b = F_w`
`implies h rho g xx pi r^2 =1/2 h rho g xx 2pi rh implies h = r`.