A smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size, each of mass $m$ , which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular velocity $\omega _0$ about its axis perpendicular to the rod and passing through its mid-point (see figure). There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is

821-1910

  • A

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

  • B

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

  • C

    $\frac{{\left( {M + 6m} \right){\omega _0}}}{M}$

  • D

    $\omega _0$

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