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

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_(C) gt W_(B) gt W_(A)` `W_(A) gt W_(B) gt W_(C)` `W_(B) gt W_(A) gt W_(C)` `W_(A) gt W_(C) gt W_(B)` Solution :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)`