Figure shows a horizontal rod AB which is free to rotate about two smooth bearing system. Two identical uniform rods each of mass m are attached to rod AB symmetrically about the centre of mass O of the rod AB. All the dimensions are given in the figure. The system is rotating with constant angular velocity $ω$ in such a way that the upper rod is coming outward from the plane of the paper in the position shown. Gravity can be assumed to be absent in the experiment. Then choose the correct option(s).

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The hinge reaction at A on the rod AB is downward

The hinge reaction at B on the rod AB is upward

The hinge reaction at B on the rod AB is downward

The angular momentum of the system about point O is NOT along the rod AB

answer is A, B, D.

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Detailed Solution

The rod attached above AB has its $a_{C M} ↓ \Rightarrow A$ net downward force must be acting on that rod and this will originate from the contact with $A B \Rightarrow$ on AB, this contact force will be upwards.
Question Image
These two normal contact forces will try to rotate AB (clockwise)

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