A girl sits stationary at the back end of a long trolley moving uniformly with speed on a smooth horizontal floor. If she gets up and runs forward on the trolly, then the speed of the center of mass of (trolley and girl) system will

CONCEPT:

Center of mass (R_CM):

• The center of mass of a system of particles is that single point that moves in the same way in which a single particle having the total mass of the system and acted upon by the same external force would move.
• Mathemically center of mass for n – particle is written as

\({\vec R_{CM}} = \frac{{{m_1}{{\vec r}_1} + {m_2}{{\vec r}_2} + {m_3}{{\vec r}_3} - - - - - - - {m_n}{{\vec r}_n}}}{{{m_1} + {m_2} + {m_3} - - - - - - - {m_n}}}\)

EXPLANATION:

• Here, the girl running on the trolley in the forward direction will exert only internal force on the running trolley.
• Only external forces can affect the center motion of the body.
• Thus, internal force here will produce no change in the velocity of the center of mass of the trolley-girl system. Thus, option 3 is correct.