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A uniform rod of length L and mass M is ...

A uniform rod of length `L` and mass `M` is lying on a frictionless horizontal plane and is pivoted at one of its ends as shown in Fig. There is no friction at the pivot. An inelastic ball of mass `m` is fixed with the rod at a distance `L//3` from `O`. A horizontal impulse `J` is given to the rod at a distance `2L//3` from `O` in a direction perpendicular to the rod. Assume that the ball remains in contact with the rod after the collision and impulse `J` acts for a small time interval `/_\t`. Now answer the following questions:

Find the resulting instantaneous angular velocity of the rod after the impulse.

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