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NEET Sample Paper NEET Sample Test Paper-58

  • question_answer
    A particle of mass \[{{m}_{1}}\] is moving with a velocity, \[{{V}_{1}}\] and another particle of mass, \[{{m}_{2}}\] is moving with a velocity,\[{{V}_{2}}\]. Both of them have the same momentum but their different kinetic energies are \[{{E}_{1}}\]and \[{{E}_{2}}\] respectively. If \[{{m}_{1}}>{{m}_{2}}\] then:

    A) \[{{E}_{1}}<{{E}_{2}}\]                    

    B) \[{{E}_{1}}{{m}_{2}}={{m}_{1}}{{E}_{2}}\]

    C) \[E=\,\,>\,{{E}_{2}}\]              

    D) \[{{E}_{1}}={{E}_{2}}\]

    Correct Answer: A

    Solution :

    [a] \[{{P}_{1}}={{m}_{1}}{{v}_{1}}{{P}_{2}}={{m}_{2}}{{v}_{2}}\] Conservation of linear momentum \[{{P}_{1}}={{P}_{2}}\] \[{{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}\] \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{v}_{2}}}{{{v}_{1}}}\] \[\frac{{{k}_{1}}}{{{k}_{2}}}\frac{\frac{1}{2}{{m}_{1}}v_{1}^{2}}{\frac{1}{2}{{m}_{2}}v_{2}^{2}}=\frac{{{m}_{1}}}{{{m}_{2}}}{{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{2}}\] \[\frac{{{k}_{1}}}{{{k}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}<1\] \[{{k}_{1}}<{{k}_{2}}\]


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