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Two particles each of mass m are connect...

Two particles each of mass m are connected by a light inextensible string and a particle of mass M is attached to the midpoint of the string. The system is at rest on a smooth horizontal table with string just taut and in a straight line. The particle M is given a velocity v along the table perpendicular to the string. Prove that when the two particles are about to collide :
(i) The velocity of M is `(Mv)/((M + 2m))`
(ii) The speed of each of the other particles is `((sqrt2M (M + m))/((M + 2m)))v`.

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