A rod of mass M and length L lies on a horizontal frictionless surface. A particle of mass m moving perpendicular to the rod with speed u strikes one end elastically and comes to rest. If m/M = 1/x, find x.
Physics · Rotational Motion · angular impulse in pure rotation and rotational collision
JEE Mains 2021

Question

A rod of mass M and length L lies on a horizontal frictionless surface. A particle of mass m moving perpendicular to the rod with speed u strikes one end elastically and comes to rest. If m/M = 1/x, find x.

Physics · Rotational Motion · angular impulse in pure rotation and rotational collision

JEE Mains 2021

G1 Physics · Accepted Answer

During the short collision, conserve angular momentum about the pivot/impact reference. Use linear impulse-momentum as needed; for an elastic collision also use kinetic-energy conservation. Substitution and simplification give 4.