Centre of mass

A hollow sphere rolls down at 30 degree incline of length 6 metre without slipping the speed of centre of mass at the bottom of the plane is(ans:6m/s:answer with steps)

Since the sphere rolls down without slipping, it is performing pure rolling motion
Hence v=Rw
Applying conservation of energy (Let the mass of sphere be m)Ei=mgh(h=6sin30 the height of top of incline from ground)
Ei=m10(6sin30)
Ei=30mEf=1/2mv2+ 1/2Iw2 ( I is the moment of inertia I=2/3 MR2 for hollow sphere)
Ef=1/2mR2w2+ 1/2(2/3mR2)w2
Ef=5/6mR2w2Solving Ei=Ef you will have
R2w2=36
Rw=6=vcm