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 about their own symmetry a…

Question

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 about their own symmetry axes. The amounts of work (W ) required to bring them to rest, would satisfy the relation [NEET 2018]

Accepted Answer

Correct answer: C. (c) Work done required to bring an object to rest is given as W= 12I ^2 where, I is the moment of inertia and is the angular velocity. Since, here all the objects spin with the same , this means, W ∝I As, I_A ( for a solid sphere )= 25MR^2 I_B ( for a thin circular disc )= 12MR^2 I_C ( fora circular ring )=MR^2 ∴W_A :W_B :W_C=I_A :I_B :I_C = 25MR^2 : 12MR^2 :MR^2 = 25 : 12 :1=4 :5 :10 ⇒W_A<W_B<W_C

Solution

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