I Launching a particle at the highest point inside a sphere

[LouysHong]

If a smooth sphere with radius a is fixed on a plane, and a particle is projected horizontally at the highest point outside/on of the sphere with speed (4ag/5)^0.5, I know that the particle will lose contact with the sphere when it makes an angle of theta with the upward vertical, where theta is cos^-1(4/5).

But what if I were to launch the particle with that speed horizontally at the highest point inside the sphere ? It seems that the particle would also lose contact at the same point ? But wouldn't the particle complete a full circle inside the sphere ?

 

[haruspex]

It seems that the particle would also lose contact at the same point ?

Why? Which way is the normal force pointing now? What equation do you get?

 

[A.T.]

It seems that the particle would also lose contact at the same point ?

If the initial speed is such that it stays in contact outside, then it would immediately loose contact inside.