question_answer

Two particles \[A\] and \[B\] start moving due to their mutual interaction only. If at any time\[t\], \[{{\vec{a}}_{A}}and\,{{\vec{a}}_{B}}\] are their respective accelerations, \[{{\vec{v}}_{A}}\,and\,{{\vec{v}}_{B}}\] are their respective velocities, and up to that time \[{{W}_{A\,}}and\,{{W}_{B}}\] are the work done on \[A\] and \[B\] respectively by the mutual force, \[{{m}_{A\,}}and\,{{m}_{B}}\] are their masses respectively, then which of the following is always correct?

A) \[{{\vec{v}}_{A}}\,+\,{{\vec{v}}_{B}}=0\]    

B) \[{{m}_{A\,}}{{\vec{v}}_{A}}+\,{{m}_{B}}{{\vec{v}}_{B}}=0\]

C) \[{{W}_{A}}\,+\,{{W}_{B}}=0\]        

D) \[{{\vec{a}}_{A}}+{{\vec{a}}_{B}}=0\]