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NEET Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति NEET PYQ-Work Energy Power and Collision

  • question_answer
    Two spheres A and B of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] respectively collide. A is at rest initially and B is moving with-velocity v along x-axis.
    After collision B has a velocity \[\frac{v}{2}\] in a direction perpendicular to the original direction. The mass A moves after collision in the direction [AIPMT (S) 2012]

    A) same as that of B

    B) opposite to that of B

    C)  \[\theta ={{\tan }^{-1}}\left( \frac{1}{2} \right)\] to the x-axis

    D) \[\theta ={{\tan }^{-1}}\left( \frac{-1}{2} \right)\]

    Correct Answer: C

    Solution :

    Here, \[{{\mathbf{p}}_{i}}={{m}_{2}}v\mathbf{i}+{{m}_{2}}\times 0\]
    \[{{\mathbf{p}}_{f}}={{m}_{2}}\frac{v}{2}\mathbf{j}+{{m}_{1}}\times {{v}_{2}}\]
    Law of conservation of momentum
                \[{{\mathbf{p}}_{i}}={{\mathbf{p}}_{f}}\]
                \[{{m}_{2}}v\mathbf{i}={{m}_{2}}\frac{v}{2}\mathbf{j}+{{m}_{2}}\times {{v}_{1}}\]
                \[{{v}_{1}}=\frac{{{m}_{2}}}{{{m}_{1}}}v\mathbf{i}+\frac{{{m}_{2}}}{{{m}_{1}}}\frac{v}{2}\mathbf{j}\]
    From this equation we can find \[\tan \theta =\frac{1}{2}\]
    \[\theta ={{\tan }^{-1}}\left( \frac{1}{2} \right)\] to the x-axis.


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