\( A \operatorname{rod} A B \) of mass \( M \) and length \( L \) is lying on a horizontal frict...

\( A \operatorname{rod} A B \) of mass \( M \) and length \( L \) is lying on a horizontal frictionless surface. A particle of mass \( m \) travelling along the surface hits the end \( A \) of the rod with a velocity \( v_{0} \) in a direction perpendicular to \( A B \). The collision is elastic. After the collision, the particle comes to rest.
(a) Find the ratio \( \mathrm{m} / \mathrm{M} \).
(b) A point \( P \) on the rod is at rest immediately after collision. Find the distance \( A P \).
(c) Find the linear speed of the point \( P \) a time \( \pi L / 3 v_{0} \) after the collision.