A cylinder has a radius 10 cm. To what height should is be filled with water so that the thrust in its walls is equal to that on its bottom ?

Answer

10 cm

Explanation

Let `rho` be the density of water, and h be the height of water in cylinder, then thrust at the bottom `F =` pressure `xx` area `= (h rho g)xx pi^2` Thrust on the walls, F'= average pressure `xx` area `F' ((rho gh)/(2)) (2pi r h) = pi r h^2 rho g`
When `F = F'`, then `h rho g xx pi r^2 =pi r h ^2 rho g`
or `h = r = 10 cm`