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(D) The system consists of two particles $A$ and $B$ moving under a mutual force of attraction. Since the mutual force of attraction is an internal fo

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(D) The system consists of two particles $A$ and $B$ moving under a mutual force of attraction. Since the mutual force of attraction is an internal force,there is no external force acting on the system $(F_{ext} = 0)$. According to the property of the centre of mass,if the net external force on a system is zero,the acceleration of the centre of mass is zero $(a_{cm} = 0)$. This implies that the velocity of the centre of mass $(v_{cm})$ remains constant. Initially,both particles $A$ and $B$ are at rest,so the initial velocity of the centre of mass is $v_{cm(initial)} = 0$. Therefore,the velocity of the centre of mass at any instant,including when the velocities of $A$ and $B$ are $v$ and $2v$ respectively,must be zero.

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of $A$ is $v$ and that of $B$ is $2v$,the velocity of the centre of mass of the system is

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