What is the minimum height of a hill, so a ball of mass m falling from it can go through a loop of radius R?

There is only one requirement for the ball to go through the loop. Its energy must be such that the centrifugal force experienced by the ball when it is at the peak of the loop is greater than gravity pulling down. If this is written down:Centripetal force = m v^2/R > mg , Therefore v > (gR)^1/2And as always, energy must be conserved, so the kinetic+potential energy at the peak of the loop must be the same as the potential energy on top of the hill (as the ball is initially stopped). Therefore, if the height of the hill is H,mgH = mg2R+1/2mv^2 > mg2R+1/2 mgRH > 5/2 RThe height of the hill must be at least 2.5 times greater than the radius of the loop.