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A wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is $I$ and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia $3I$ initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:
(1) $\frac{5}{6}$
(2) $\frac{1}{4}$
(3) 0
(4) $\frac{3}{4}$
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