let h be the height of liquid column of density `rho` in the cylindrical vessel of radius r. The froce acting on the bottom of vessel = weight of liquid filled in cylinder ` = mg = (pi r^2 h rho)g` …. (i) The area of walls incontact with liquid ` = 2pi rho` Average pressure of liquid on walls is `P = ("pressure at bottom "+ "pressrue at top of liquid column")/(2)`
` = (rho gh _ 0)/(2) = (rho gh)/(2)`
Force on the walls of vessel `= (rho g h)/(2) xx 2pi r h = pi rho grh^2` ..... (ii)
As per question the forces (i) and (ii) are equal so, `pi r^2 h rho g = pi rho g rh^2` or `h =r` it means height of liquid coluum in vessel should be equal to its radius.