A cylinder has a radius 20 cm. To what height should it be filled with water so that thrust in its walls is equal to that on its bottom? Find the mass of water filled in cylinder.

Explanation

let h be the hieght of water filled in cylinder and `rho` be the density of water. Then
thrust at the bottom of vessel
`F= "pressure cc area" = (h rho g) xx pi r^(2)`
Thrust on the walls of vessel,
`F'=` average pressure `xx` area
`F' = ((h rho g)/(2)) xx (2 pi r h) = pi rh^(2) rho g`
when `F=F'`, then `h rho g xx pi r^(2) = pi r h^(2) rho g`
or `h=r = 20cm`.