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.

Options

A. `W_(A)gtW_(C)gtW_(B)`
B. `W_(C)gtW_(B)gtW_(A)`
C. `W_(B)gtW_(A)gtW_(C)`
D. `W_(A)gtW_(B)gtW_(C)`

Answer

B

Explanation

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)`