A uniform rod of mass m and length l can rotate freely on a smooth horizontal plane about a vertical axis hinged at point H. A point mass having same mass m coming with an initial speed u perpendicular to the rod, strikes the rod in-elastically at its free end. Find out the angular velocity of the rod just after collision?

Explanation

Angular momentum is conserved about H because no external force is present in horizontal plane which is producing torque about H.
`m u l = ((m l ^(2))/(3) + ml^(2)) omega rArr w = (3u)/(4l)`