2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 25

  • question_answer
    Two particles of equal mass have velocities \[\overset{\to }{\mathop{{{v}_{1}}}}\,=2\hat{i}\,\,m/s\] and\[\overset{\to }{\mathop{{{v}_{2}}}}\,=2\hat{j}\,\,m/s\]. First particle has an acceleration \[\overset{\to }{\mathop{{{a}_{1}}}}\,=(3\hat{i}+3\hat{j})\,m/{{s}^{2}}\] 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 :

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


You need to login to perform this action.
You will be redirected in 3 sec spinner