How to solve the physics problem in the picture?

Question

A uniform horizontal circular disc of mass M and radius R can freely rotate about a vertical axle passing through its centre. A particle of mass m is initially placed near the centre of the disc in a smooth groove made along the radius of the disc as shown. An initial angular velocity w0 is imparted to the disc. Find the angular velocity of the disc, when the particle reaches the other end of the groove.

Answer 1

As external torque is zero just apply conservation of angular momentum.

I1W1 = I2W2.

So (MR²/2)w0 = (MR²/2 + mR²)w.

So new w = Mw0/(M+2m).