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)



  • @mkumar-mkumar

    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=30m

    Ef=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=5/6mR2w2

    Solving Ei=Ef you will have
    R2w2=36
    Rw=6=vcm


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