Question

Considering there is no friction , find the minimum angle `\alpha` for which the ball gets out of the hole.(answer: `\alpha=60` ; I want to know the full solution) (?)

Answer 1

Clearly here the `mg sin alpha` component of the weight of the body tries to rotate it w.r. t the point at which the body touches the inclined plane and it's `mg cos alpha` prevents it from doing so.
So at least both of them should be equal to allow the body move with uniform velocity.
So,considering torque acting on the body w.r.t the point of contact we get,
`mg sin alpha` `R/2` = `mg cos alpha` `{R^2-(R/2)^2}`
So `tan alpha` will be √3
I.e alpha will be 60 degrees