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 :
Option: 1 \frac{5}{6}
Option: 2 \frac{1}{4}
Option: 3 0
Option: 4 \frac{3}{4}

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