A thin smooth rod of length L and mass M is rotating freely with angular speed `omega_(0)` about an axis perpendicular ot the rod and passing through its centre. Two beads of mass m and negligible sizer are at the center of the rod intially. The beads are free to slide along the rod. the angular speed of the system, when the beads reach the oppsite ends of rod, will be :

Options

A. `(Momega_(0))/(M + 6m)`
B. `(Momega_(0))/(M + 3m)`
C. `(M omega_(0))/(M + 2m)`
D. `(M omega_(0))/(M + m)`

Answer

A

Explanation

Conservation of angular momentum `[(ML^(2))/12 + 2m(0)^(2)] omega_(0)[(ML^(2))/12 + 2 xx m(L/2)^(2)]omega, omega = (Momega_(0))/(M+6m)`