Initial angular velocity is \(\omega_1=20\,rad / s\)

Moment of Inertia of disc is \(I _1= mr ^2 / 2=\frac{1 \times 0.01}{2}\,kgm ^2=0.005\,kgm ^2\)

The new moment of inertia when a particle is placed on the circumference i.e at a distance \(r\) from the axis is \(I _2= I _1+ Mr ^2=0.005+0.5\,kg \times(0.1)^2=0.01\,kgm ^2\) In this process the the angular momentum, \(J = I \omega\) will remain conserved so \(I _1 \omega_1= I _2 \omega_2\)

so the new angular velocity, \(\omega_2=\frac{ I _1}{ I _2} \omega_1=\frac{0.005}{0.01} 20=10\, rad / s\)