question_answer

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:                                                                                       [JEE Main 9-4-2019 Afternoon]

A)  \[\frac{M{{\omega }_{0}}}{M+3m}\]   

B)       \[\frac{M{{\omega }_{0}}}{M+m}\]

C)  \[\frac{M{{\omega }_{0}}}{M+2m}\]   

D)       \[\frac{M{{\omega }_{0}}}{M+6m}\]

Correct Answer: D

Solution :

[d] Applying angular momentum conservation, about axis of rotation