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NEET AIPMT SOLVED PAPER 2003

  • question_answer
                    A stationary particle explodes into two particles of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] which move in opposite directions with velocities \[{{v}_{1}}\] and \[{{v}_{2}}\]. The ratio of their kinetic energies \[{{E}_{1}}/{{E}_{2}}\] is:                                                              

    A)                 1

    B)                 \[{{m}_{1}}{{v}_{2}}/{{m}_{2}}{{v}_{1}}\]             

    C)                 \[{{m}_{2}}/{{m}_{1}}\]

    D)                 \[{{m}_{1}}/{{m}_{2}}\]

    Correct Answer: C

    Solution :

                           Key Idea: For a exploding body, linear momentum is conserved.                 From conservation of linear momentum,                 \[{{P}_{inititial}}={{P}_{final}}\]                 \[0={{m}_{1}}{{v}_{1}}-{{m}_{2}}{{v}_{2}}\]                 \[or{{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}\]                 \[or\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}....(i)\]                 Thus, ratio of kinetic energies,                  \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{\frac{1}{2}{{m}_{1}}v_{1}^{2}}{\frac{1}{2}{{m}_{2}}v_{2}^{2}}=\frac{{{m}_{1}}}{{{m}_{2}}}\times {{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{2}}\]                 \[=\frac{{{m}_{2}}}{{{m}_{1}}}\]


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