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Work, Energy And Power

Question
CBSEENPH11017298

A sphere of mass m moving with velocity u collides with stationary sphere of same mass. If e is the coefficient of restitution, then find the velocities of two masses after collision.

Solution

Let v1 and v2 be the velocities of colliding body and target body after collision respectively.
Applying conservation of momentum, 
               straight m space straight u plus straight m cross times 0 equals straight m space straight v subscript 1 plus straight m space straight v subscript 2  
rightwards double arrow                  straight v subscript 1 plus straight v subscript 2 equals straight u                    ...(1) 
Using the definition of coefficient of restitution, 
                      straight e equals fraction numerator straight v subscript 2 minus straight v subscript 1 over denominator straight u end fraction 
rightwards double arrow          straight v subscript 2 minus straight v subscript 1 equals straight e space straight u                           ...(2) 
Solving (1) and (2), we get
           space space straight v subscript 2 equals fraction numerator straight e plus 1 over denominator 2 end fraction straight u  and  straight v subscript 1 equals fraction numerator straight e minus 1 over denominator 2 end fraction straight u