A rod AB 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 AB. The collision in elastic. After the collision the particle comes to rest
(a). Find the ratio `m//M`
(b). A point P on the rod is at rest immediately after collision find the distance AP.
(c). Fid the linear speed of the point P a time `piL//3v_(0)` after the collision.