I was solving a problem
Here is the solution
The velocity of that small disc is with respect to hemisphere frame .
And the velocity of that of that hemisphere is in ground frame.
So let's conserve momentum in direction After this conserving energy as always
And the last equation normal to the inclined plane when it losses contact normal reaction will be zero
Which gives the equation
After solving these 3 equations patiently gives
The only reasonable value of seems to be