JEE Main & Advanced Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति Sample Paper Topic Test - Work Energy Power

  • question_answer
    Body of mass m moving with a velocity\[v\]in the \[+\text{ }ve\]X direction collides with a body of mass M moving with a velocity V in the \[+\text{ }ve\]Y direction. The collision is perfectly inelastic. Mark out the correct statement(s) w.r.t. this situation.

    A) The magnitude of momentum of the composite body is\[\sqrt{{{(mv)}^{2}}+{{(MV)}^{2}}}\]

    B) The composite body moves in a direction making an angle \[\theta ={{\tan }^{-1}}\left( \frac{MV}{mv} \right)\]with \[+\text{ }ve\]X-axis.

    C) The loss of kinetic energy due to collision

    D) All of the above

    Correct Answer: D

    Solution :

    [d] As no external force is acting momentum of the system remains conserved, i.e., \[{{\vec{P}}_{f}}=mv\hat{i}+mV\hat{j}\]
      \[\Rightarrow \]\[\tan \theta =\frac{MV}{mv}\]
      Loss in \[KE==\Delta K\]
      \[=\frac{m{{v}^{2}}}{2}+\frac{M{{V}^{2}}}{2}-\frac{1}{2}\left[ \frac{{{(mv)}^{2}}+{{(MV)}^{2}}}{M+m} \right]\]
                \[=\frac{Mm}{2\,(M+m)}\times ({{V}^{2}}+{{v}^{2}})\]

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