There object, `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 amount of work `(W)` required ot bring them to rest, would satisfy the relation

Options

A. `W_(B) gt W_(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

Work done required to bring them rest
`Delta W=Delta KE`
`DeltaW=(1)/(2)Iomega^(2)`
`DeltaW prop I` for same `omega`
`W_(A) : W_(B) : W_(C) =(2)/(5)MR^(2) : (1)/(2)MR^(2) : MR^(2)`
`=(2)/(5): (1)/(2):1`
`=4:5:10`
`implies W_(C) gt W_(B) gt W_(A)`