A body slides down an inclined plane after being released from rest from a height h and finally it describes a circle of radius r instead of travelling along a horizontal floor. For what minimum value of h , can the particle describe that motion ? Ignore friction.

Explanation

After descending along the inclined plane ,the body can describe the circular path if the velocity of the body at the lowest point B of the circular path is , at least, `v=sqrt(5gr)` [Fig.1.35].

Kinetic energy of the body at the point B
`=1/2 mv^2=1/2 m*5gr=5/2 mgr`
The falling body will acquire this kinetic energy in exchange of the potential energy that it possesses at the height h.
So, `5/2mgr=mgh or, h=5/2r`.