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

The correct option is D $\text{Zero}$
Given:
The initial velocity of particles A and B is zero as both particles are at rest initially.
$\Rightarrow \text{COM}\text{is at rest initially}\Rightarrow (V_{com}{)}_{initial}=0$

As external force, $F_{ext}=0\Rightarrow a_{com}=0$
$\Rightarrow \text{COM}$ will remain at rest even when particles A and B starts moving towards each other under the influence of internal force (mutual force of attraction)
$\therefore (V_{com}{)}_{final}=0$