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A homogenous rod of length l=etax and ma...

A homogenous rod of length `l=etax` and mass `M` is lying on a smooth horizontal floor. A bullet of mass m hits the rod at a distance `x` from the middle of the rod at a velocity `v_(0)` perpendicular to the rod and comes to rest after collision. If the velocity of the farther end of the rod just after the impact is in the opposite direction of `v_(0)`, then:

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