Let V be the velocity and q is the angle made by the radius vector with the vertical at the instant when the ball break off the sphere. Let it happens at a vertical height h below the top. Therefore We have mgh =
1
2
mv2 +
1
2
Iω2 ⇒ mg (R + r) (1 - cosθ) =
1
2
m (rω)2 +
1
2
Iω2 .... (i) At the break off, mg cosθ = N +
mv2
(R+r)
Substituting N = 0 and v = rω we get mg cosθ =
m(rω)2
(R+r)
... (ii) Solving equations (i) and (ii), we get ω = √