Bro..try using mv^2/r waala method (wrt sphere frame)..getting different answer from there..
Your answer is correct btw
Bro @pushkar_2020 Use this method for time saving
Also that method that you have mentioned has a confusing point
As in the frame of the sphere the sphere is still rotating with αR=a_c so the surface of the sphere
If you take that zero then initially the particle has a velocity in the opposite direction of the rotation of the sphere and this makes the the problem hard to tackle furthermore
Use v(in mv^2/r) by considering relative motion(sphere) of particle