Three objects, A (a solid sphere), B (a thin circular disc) 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_(B) gtW_(A) gt W_(C)`
B. `W_(A) gt W_(B) gt W_(C)`
C. `W_(C) gt W_(B) gt W_(A)`
D. `W_(A) gt W_(C) gt W_(B)`

Answer

C

Explanation

According to work-energy theorem we can write
`DeltaW=DeltaK.E.`
`DeltaW=(1)/(2)Iomega^(2)`
`DeltaWpropI`
`W_(A):W_(B):W_(C)=(2)/(5)MR^(2):(1)/(2)MR^(2):MR^(2)`
`=(2)/(5):(1)/(2):1=4:5:10`
`impliesW_(C)gtW_(B)gtW_(A)`
Hence option (c) is correct.