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Question:

The total kinetic energy of the ring is

12Mω²⁰(R−r)²

Mω²⁰R²

32Mω²⁰(R−r)

Mω²⁰(R−r)²

Solution:

K=1/2Mv²c+1/2Icω²
K=1/2M(ω²(R−r))²+1/2MR²ω²⁰
K=1/2Mω²⁰R²(1−r/R)²+1/2Mω²⁰R²
r<<Rr/R→0
K=1/2Mω²)R²+1/2Mω²)R²
K=Mω²⁰R²
Hence correct answer is D.