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Statement of a problem № 3159

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A particle of mass m with initial velocity u makes an elastic collision with a particle of mass M initially at rest. After the collision the particles have equal and opposite velocities. Find (a) the ratio M/m; (b) the velocity of centre of mass; (c) the total kinetic energy of the two particles in the centre of mass; and (d) the final kinetic energy of m in the laboratory system.

Solution:
A particle of mass m with initial velocity u makes an elastic collision with a p

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