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.