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Work, Energy And Power

Question
CBSEENPH11017289

Show that when the colliding body is very-very light as compared to target and target is at rest, then colliding body rebounds with same speed.

Solution
When the two bodies collide elastically, the velocities of two bodies after collision are given by, 

              straight v subscript 1 equals fraction numerator left parenthesis straight m subscript 1 minus straight m subscript 2 right parenthesis straight u subscript 1 plus 2 straight m subscript 2 straight u subscript 2 over denominator straight m subscript 1 plus straight m subscript 2 end fraction
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Here, we have
                 straight m subscript 1 less than less than less than straight m subscript 2 
Therefore, 
                   straight m subscript 1 minus straight m subscript 2 almost equal to negative straight m subscript 2 
and              straight m subscript 1 plus straight m subscript 2 almost equal to straight m subscript 2 
Thus,  straight v subscript 1 almost equal to fraction numerator negative straight m subscript 2 straight u subscript 1 plus 2 straight m cross times 0 over denominator straight m subscript 2 end fraction almost equal to negative straight u subscript 1 
Hence, we can see that the colliding body rebounds with the same speed.