A uniform ball of radius r rolls without slipping down from the top of a sphere of radius R. The angular velocity of the ball when it breaks from the sphere is

mv2(R+r)=mgcosθmgh=12mv2+12Iω2mg(R + r) (1 – cosθ) = 12mv2+15mv2=710mv2107mg(R+r)(1−cosθ)=mgcosθmv2=107mg(R + r)(1 – cosθ)107=177cosθ or cosθ=1017v=g(R+r)cosθ=107g(R+r)and ω=vr=10g(R+r)17r2