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) (?)

my computermy computer

1 Answer
Jan 10, 2018

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