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_(C) gt W_(B) gt W_(A)`
B. `W_(A) gt W_(B) gt W_(C)`
C. `W_(B) gt W_(A) gt W_(C)`
D. `W_(A) gt W_(C) gt W_(B)`

Answer

A

Explanation

Work done required to bring a object to rest
`Delta W = Delta KE`
`Delta W = (1)/(2) I omega^(2)` , where I = moment of inertia
For same `omega , Delta W prop I`
For a solid sphere , `I_(A) = (2)/(5) MR^(2)`
For a thin circular disk , `I_(B) = (1)/(2) MR^(2)`
For a circular ring , `I_(C) = MR^(2)`
`therefore I_(C) gt I_(B) gt I_(A) therefore W_(C) gt W_(B) gt W_(A)`