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KVPY Sample Paper KVPY Stream-SX Model Paper-31

  • question_answer
    Two particles of equal mass have velocities \[{{\overrightarrow{v}}_{1}}=2\overset{\hat{\ }}{\mathop{i}}\,m/s\] and\[{{\overrightarrow{v}}_{2}}=2\overset{\hat{\ }}{\mathop{j}}\,m/s\]. First particle has an acceleration\[{{\overrightarrow{a}}_{1}}=\,(3\overset{\hat{\ }}{\mathop{i}}\,+\,3\overset{\hat{\ }}{\mathop{j}}\,)\,m/{{s}^{2}}\], while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a:

    A) circle

    B) parabola

    C) straight line       

    D) ellipse

    Correct Answer: C

    Solution :

    \[{{\overrightarrow{v}}_{com}}=\frac{{{m}_{1}}{{\overrightarrow{v}}_{1}}+{{m}_{2}}{{\overrightarrow{v}}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]
    \[=\frac{\overrightarrow{{{v}_{1}}}+{{\overrightarrow{v}}_{2}}}{2}\]                \[\left( {{m}_{1}}={{m}_{2}} \right)\]
    \[=\left( \overset{\hat{\ }}{\mathop{i}}\,+\overset{\hat{\ }}{\mathop{j}}\, \right)m/s\]
    Similarly \[{{\overrightarrow{a}}_{com}}=\frac{\overrightarrow{a}+{{\overrightarrow{a}}_{2}}}{2}=\frac{3}{2}\left( \overset{\hat{\ }}{\mathop{i}}\,+\overset{\hat{\ }}{\mathop{j}}\, \right)m/{{s}^{2}}\]
    Since, \[{{\overrightarrow{v}}_{com}}\] is parallel to \[{{\overrightarrow{a}}_{com}}\] the path will be a straight line.


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