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 ${\mathrm{\omega }}_0$, about an axis perpendicular to rod and passing through the mid-point of rod. There are no external forces. When

the beads reach the ends of the rod, the angular velocity of the system is

• A

  $\left(\frac{\mathrm{M}}{\mathrm{M}+3\mathrm{m}}\right){\mathrm{\omega }}_0$

• B

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

• C

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

• D

  ${\mathrm{\omega }}_0$