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

The correct option is A $zero$
Zero, according to newton law of motion if body is at rest and no external force is acting then body will be at rest until external force acts.

As we know both of these are moving due to their mutual attraction so velocity of center of mass will be constant ,i.e. $zero$.