A sphere of mass m and radius `r = sqrt3`m is placed inside a container with flat bottom and slant sidewall as shown in the figure. The sphere touches the slant wall at point A and the floor at point B. It does not touch any other surface. The container, along with the sphere, is rotated about the central vertical axis with angular speed `omega`. The sphere moves along with the container, i.e., it is at rest relative to the container. The normal force applied by the bottom surface and the slant surface on the sphere are `N_(1)` and `N_(2)` respectively. There is no friction.
(a) Find the value of `omega` above which `N_(2)` becomes larger than `N_(1)`
(b) Find the value of `omega` above which the sphere leaves contact with the floor.

Answer

`sqrt((g)/(sqrt3))`
(b) `sqrt(3sqrt3g)`