For full points I would like to see an explanation and a correct answer. Thank y

Question

For full points I would like to see an explanation and a correct answer.

Thank you.

Three objects of masses m, M, and m (where m and M are unknowns ) are placed on a frictionless horizontal surface. Mass a is initially moving along the line joining the centers of the objects with an initial velocity of v n/s in the direction indicated in the diagram and Masses B and C are at initially at rest. The velocity of the center of mass of the SYSTEM OF THREE MaSSES (that is, the system including all three masses) is assume all collisions arc elastic. diagram below represents the final velocities of the three objects after the last possible collision has occurred Which of the following correctly gives M, the mass of B, in terms of m?

Explanation / Answer

C) M = 2m

vcm = v0/4

and vcm = m*v0/(M+2m)

==> v0/4 = m*v0/(M+2m)

==> 4m = 2m +M

==> M = 2m

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