Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed omega about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation.

Three objects, A : (a solid sphere), B : (a thin circular disk) and C

1.	Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed omega about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation.
Answer» `W_(A)gtW_(C)gtW_(B)` `W_(C)gtW_(B)gtW_(A)` `W_(B)gtW_(A)gtW_(C)` `W_(A)gtW_(B)gtW_(C)` Solution :Work-energy theorem, `W=DeltaK` `therefore W=(1)/(2)Iomega^(2)` `therefore WpropI [because (1)/(2),W" SIMILAR"]` Now, for solid sphere, `I_(A)=(2)/(5)MR^(2)=0.4 MR^(2)` For disc, `I_(B)=(1)/(2)MR^(2)=0.5MR^(2)` for RING, `I_(C)=MR^(2)=MR^(2)` `therefore I_(C)gtI_(B)gtI_(A)` because `W_(C)gtW_(B)gtW_(A)`