a good problem

this is a problem from the book Richard Feynman's lectures on physics

let the body be kept on the top most point of the sphere.

let us asuume that the sphere is kept on a flat ground. taking the point of contact of the sphere with ground as the aero potential energy line,

the potential energgy of the body at top most point =mg(2r) where `r` is the radius of the sphere.

now let this body fly off from the sphere at a point the radius vector to which makes an angle α with the vertical.

at that point where body flies off , we have

mv2/r=mgcosα ----( 1)

by conservation of energy we have

mg(2r)=mgr(1+cosα)+1/2mv2 ---- (2)

from (1) and (2) , we get

cosα=2/3

therefore the body flies off at a point when he radius vector makes an angle cos-12/3 with the vertical.