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JEE Main & Advanced AIEEE Solved Paper-2013

  • question_answer
    This question has statement I and Statement II. Of the four choice given after the statements, choose the one that best describes the two statements. Statement - I: A Point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as \[f\left( \frac{1}{2}m{{v}^{2}} \right)\]then\[f=\left( \frac{m}{M+m} \right)\] Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.     AIEEE Solevd Paper-2013

    A) Statement - I is true, Statement - II is true, statement - II is a correct explanation of Statement - I

    B) Statement - I is true, Statement - II is true, statement - II is not a correct explanation of Statement - I

    C) Statement - I is true, Statement - II is false

    D) Statement - I is false, Statement - II is true

    Correct Answer: D

    Solution :

    Maximum energy loss when inelastic collision takes place \[mv=(m+M)v\prime \] \[v\prime =\frac{m}{m+M}v\] \[{{k}_{i}}=\frac{1}{2}m{{v}^{2}}\] \[{{k}_{f}}=\frac{1}{2}(m+M)v{{'}^{2}}=\frac{1}{2}(m+M)\frac{{{m}^{2}}{{v}^{2}}}{{{(m+M)}^{2}}}\] \[=\frac{1}{2}m{{v}^{2}}\left( \frac{m}{M+m} \right)\] Loss of energy\[={{k}_{i}}-{{k}_{f}}=\frac{1}{2}m{{v}^{2}}\left[ 1-\frac{m}{M+m} \right]\] \[=\frac{M}{M+m}\times \frac{1}{2}m{{v}^{2}}\]


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