Problem 1.198

A ball of mass $m$ moving with velocity $v_{0}$ 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 $\tilde{M}$ 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.