A ring of mass M and radius R is rotating about its axis with angular velocity ω . Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of thi

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A ring of mass M and radius R is rotating about its axis with angular velocity ω . Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be :

TestHub · Accepted Answer

Kinetic energy (rotational) ​ K R ​ = 2 1 ​ I ω 2 Kinetic energy (translational) ​ K T ​ = 2 1 ​ Mv 2 ​ ( v = R ω ) M.I. (initial) ​ I ring ​ = MR 2 ; ω initial ​ = ω M.I. (new) ​ I ′ (system) ​ = MR 2 + 2 mR 2 ω ( system) ′ ​ = M + 2 m M ω ​ ​ Solving we get loss in K.E. = ( M + 2 m ) Mm ​ ω 2 R 2

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