The following figure shows two situations in which a uniform round rigid body is released from rest from the positions shown, such that it is just able to loop the loop without leaving contact with the track. Assuming that radius of the track is large in comparison to the radius of round body, the ratio $$h1/h2$$

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Infinity Learn · Accepted Answer

$$Case-1$$ : $$mgh1=($$$$KE$$$$)trans=Ktrans=12mv2Whole$$ gravitational potential energy is converted into translational K.E. only.$$Case-2$$ : $$mgh2=Ktrans+Krot=12mv2+12Icm$$ω$$2Some$$ part of gravitational potential energy will be converted into rotational K.E. also.Hence in second case, greater height is required.

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