Initial angular velocity of a circular disc of mass M is ω₁ Then two spheres of mass m are attached gently two diametrically opposite points on the edge of the disc what is the final angular velocity of the disc? 

[M / (M + 2m)] ω₁  

Conservation of Angular Momentum : I₁ω₁ = I₂ω₂ 

ω₂ = (I₁ / I₂)ω₁ 

For circular disc : I = [(MR²) / 2]

I₁ = [(MR²) / 2]

when two spheres of masses are attached then total mass is M + 2m

I₂ = [(M + 2m) / 2]R² 

hence ω_2 = [{(MR²) / 2} / {{(M + 2m) / 2}]R²}](ω₁)

= [M / (M + 2m)]ω_1­­