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A rod lying on a frictionless horizontal...

A rod lying on a frictionless horizontal surface is initially given an anglular velocity `omega` about vertical axis which passes through center of mass. The centre of mass is at rest but not fixed. The length of the rod is L. Subsequently, end A of the rod collides with nail P, which is near to A such that end A becomes stationery immediately after impact. Velocity of end B just after collision will be

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