A vertically oriented uniform \( \operatorname{rod} \) of mass \( M \) and length \( l \) can ro...

A vertically oriented uniform \( \operatorname{rod} \) of mass \( M \) and length \( l \) can rotate about its upper end. A horizontally flying bullet of mass \( m \) strikes the lower end of the rod and gets stuck in it; as a result, the rod swings through an angle \( \alpha \). Assuming that \( m \), find :
at what distance \( x \) from the upper end of the rod the bullet must strike for the momentum of the system "bullet-rod" to remain constant during the impact.