AIIMS 2018 Physics Center of Mass MCQ Question

The velocity of the center of mass (V_cm) of a system is given by the formula $V_{cm} = \frac{m_P v_P + m_Q v_Q}{m_P + m_Q}$, where $m_P$ and $m_Q$ are the masses of objects P and Q, and $v_P$ and $v_Q$ are their respective velocities. Since both objects are moving towards each other, we can assign $v_P = v$ and $v_Q = -2v$ (taking the direction of P's velocity as positive), leading to $V_{cm} = \frac{m_P v - m_Q (2v)}{m_P + m_Q}$. If the masses are equal, this results in $V_{cm} = 0$, indicating that the center of mass remains stationary, thus confirming option D as correct. Other options are incorrect because they suggest a non-zero velocity for the center of mass, which contradicts the principle of conservation of momentum in a closed system where both objects are initially at rest.