Question

A ball of mass m moving with velocity v_o experiences a head-on elastic collision with one of the spheres of a stationary rigid dumbbell as whown in Fig. 1.50. The mass of each sphere equals m/2, and the distance between them is l. Disregarding the size of the spheres, find the proper angular momentum M of the dumbbell after the collision, i.e. the angular momentum in the reference frame moving translationally and fixed to the dumbbell's centre of inertia.

Answer 1

From conservation of linear momentum along the direction of the incident ball for the system consists with colliding ball and phhere

mv₀=mv'+m/2v₁   (1) 

where v' and v₁ are the velocities of ball and sphere 1 respectively after collision. (Remember that the collision is head on). 

As the collision is perfectly elastic, from the definition of co-efficient of restitution,