A thin smooth rod of length L and mass M is rotating freely with angular speed $\omega $0 about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system , when the beads reach the opposite ends of the rod, will be :-

Question

A thin smooth rod of length L and mass M is rotating freely with angular speed $\omega $₀ about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system , when the beads reach the opposite ends of the rod, will be :-

${{M{\omega _0}} \over {M + 3m}}$

${{M{\omega _0}} \over {M + m}}$

${{M{\omega _0}} \over {M + 6m}}$

${{M{\omega _0}} \over {M + 2m}}$

Solution

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