A small insect is climbing slowly along the inner wall of a hemispherical bowl of radius R. The insect is unable to climb beyond `theta = 45^(@)`. Whenever it tries to climb beyond `theta = 45^(@)`, it slips.
(a) Find the minimum angular speed `omega` with which the bowl shall be rotated about its vertical radius so that the insect can climb upto `theta = 60^(@)`.
(b) Find minimum `omega` for which the insect can move out of the bowl.

Answer

`sqrt((g)/(R) (2(sqrt3-1))/(sqrt3(sqrt3 + 1)))`
(b) `sqrt((g)/(R))`