A thin rod of mass 0 . 9   kg and length 1   m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0 . 1   kg moving in a straight line with velocity 80   m   s - 1 hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad   s - 1 ) of the rod immediately after the collision will be …&he

Step-by-step solution

Given, Mass of the rod, M = 0 . 9   kg Mass of particle, m = 0 . 1   kg Length of the rod, l = 1   m Velocity of particle, v = 80   m   s - 1 No external torque acting on the system of rod and particle, so angular momentum of system about the suspension is conserved, i.e.; L i = L f ⇒ m v l = I ω     . . . ( 1 ) Where, I is the momentum of inertia of rod and particle system, ω is the angular velocity of system just after the collision. ⇒ m v l = M l 2 3 + m l