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Work, Energy And Power

Question
CBSEENPH11017293

A neutron travelling with a velocity v and energy E collides elastically with a nucleus of mass number A. Find the energy retained by the neutron after collision.

Solution
The fractional energy retained by colliding mass is, 
straight K subscript 1 over straight K equals open parentheses fraction numerator straight m subscript 1 minus straight m subscript 2 over denominator straight m subscript 1 plus straight m subscript 2 end fraction close parentheses squared 
Here, we have
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#6 {main}</pre>,  and    
K.E = E 
Therefore, 
            straight K subscript 1 over straight E equals open parentheses fraction numerator straight m subscript 1 minus Am subscript 1 over denominator straight m subscript 1 plus Am subscript 1 end fraction close parentheses squared equals open parentheses fraction numerator 1 minus straight A over denominator 1 plus straight A end fraction close parentheses squared 
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#6 {main}</pre> , is the energy retained by the neutron after collision.