A uniform sphere of radius r rolls without slipping down the top of a sphere of radius R. The initial velocity of the sphere is negligible. The angular velocity of the moving sphere at the moment when it breaks off from the other sphere is

When the line joining the centers of the two spheres makes an angle θ with the vertical, thenmgcos⁡θ−N=mv2R+rWhen the contact breaks off N= 0mgcos⁡θ=mv2R+r=mω2r2R+r  ⋯(1)[∵v=ωr]From COE principlemg(R+r)=mg(R+r)cos⁡θ+12mv2+12Iω2mg(R+r)=(R+r)mω2r2R+r+mω2r22+12⋅25mr2ω2 or g(R+r)=1710ω2r2∴ω=10g(R+r)17r2