First slide
Rolling motion

A small object of uniform density rolls up a curved surface with an initial velocity 'υ'. It reaches upto a maximum height of 3υ24gwith respect to the initial position. The object is


The kinetic energy of the rolling object is converted into potential energy at height


So by the law of conservation of mechanical energy, we have

12Mv2+12Iω2=Mgh 12Mv2+12IvR2=Mg3v24g           ω=vR 12Iv2R2=34Mv212Mv2 12Iv2R2=14Mv2   or   I=12MR2

Hence, the object is disc.

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