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NEET AIPMT SOLVED PAPER SCREENING 2004

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

    C) \[{{E}_{1}}>{{E}_{2}}\]          

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

    Correct Answer: A

    Solution :

    Kinetic energy is given by \[E=\frac{1}{2}m{{v}^{2}}=\frac{1}{2m}{{(mv)}^{2}}\] but\[mv=\] momentum of the particle \[=p\] \[\therefore E=\frac{p}{2m}\]           or            \[p=\sqrt{2mE}\] Therefore,\[\frac{{{p}_{1}}}{{{p}_{2}}}=\sqrt{\frac{{{m}_{1}}{{E}_{1}}}{{{m}_{2}}{{E}_{2}}}}\] but it is given that, \[{{p}_{1}}={{p}_{2}}\] \[\therefore \]\[{{m}_{1}}{{E}_{1}}={{m}_{2}}{{E}_{2}}\] or\[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\] Now \[{{m}_{1}}>{{m}_{2}}\] or\[\frac{{{m}_{1}}}{{{m}_{2}}}>1\] ...(ii) Thus, Eqs. (i) and (ii) give \[\frac{{{E}_{1}}}{{{E}_{2}}}<1\] or\[{{E}_{1}}<{{E}_{2}}\]


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