Three small spheres, A, B and C, of masses m, km and 6m respectively, have the same

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Three small spheres, A, B and C, of masses m, km and 6m respectively, have the same radius. They are at rest on a smooth horizontal surface, in a straight line with B between A and C. The coefficient of restitution between A and B is 1/2 and the coefficient of restitution between B and C is e. Sphere A is projected towards B with speed u and is brought to rest by the subsequent collision. Show that k = 2.

Given that there are no further collisions after B has collided with C, show that e ≤ 1/3.

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