Question

A rod of length / and mass 4m lies on a frictionless horizontal surface on which it is free to move anyway. A ball of mass m moving with speed v. Collides with the rod at one of the ends If ball comes to rest immediately after collision find out angular velocity u) of rod just after collision

Answer 1

The angular momentum of the system consisting of ball and rod is constant as no external force is acting.

Hence, initial angular momentum and final angular momentum is conserved about center of mass of rod.

Final angular momentum of ball is 0 as it comes to rest.

Hence, $mv\frac{l}{2}=I\omega =\frac{4m{l}^2}{12}\omega$

$⟹\omega =\frac{3v}{2l}$