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Work, Energy And Power

Question
CBSEENPH11017291

A body of mass m1 moving with velocity u collides elastically with mass m2 at rest. Find the fractional energy transferred to mass m2 after collision. |

Solution
Velocity of mass m2 after collision is given by,

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#6 {main}</pre> 
Here, we have
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#6 {main}</pre> and straight u subscript 2 equals 0 
Therefore,
              straight v subscript 2 equals fraction numerator 2 straight m subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction straight u 
∴ Kinetic energy of mass straight m subscript 2 after collision is,
                          space space space space straight K subscript 2 equals 1 half straight m subscript 2 straight v subscript 2 superscript 2 equals 1 half straight m subscript 2 open parentheses fraction numerator 2 straight m subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction close parentheses squared straight u squared 
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#6 {main}</pre> 
Since initially mass m2 is at rest, therefore kinetic energy transferred to mass m2 is equal to the kinetic energy of mass m2 after the collision. 
Therefore,
Fractional energy transferred is, 
straight K subscript 2 over straight K equals fraction numerator begin display style 1 half end style begin display style fraction numerator 4 straight m subscript 1 squared straight m subscript 2 over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis squared end fraction end style straight u squared over denominator begin display style 1 half end style straight m subscript 1 straight u squared end fraction equals fraction numerator 4 straight m subscript 1 straight m subscript 2 over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis squared end fraction