Groovy groove

We have a disk of mass MM and radius RR placed on a horizontal plane. A cylindrical groove of radius rr is made on a diameter.Now a sphere of mass mm and radius rr is placed in the groove at the circumference of the disk.

At t=0t=0 the whole system is rotated with an angular velocity 1rad/s1 rad/s as shown in the figure.Also at the same time the sphere was projected with a velocity vv towards the centre of the disk.Find the minimum velocity vv of the sphere such that it is able to reach the other end of the groove.

Details and Assumptions

1)rR1)r\ll R

2)M=2kg2)M=2kg

3)m=3Kg3)m=3Kg

4)R=2m4)R=2 m

5)5)The disk is fixed about it's centre that is it can only rotate

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