Answer
The correct answer is:
(d) It moves with a speed of $\frac{1}{2}v$ away from A.
Work Step by Step
Let $m$ be the mass of each particle. We can find the velocity of the center of mass:
$v_{cm} = \frac{mv_A+mv_B}{m+m} = \frac{0+m~v}{2m} = \frac{v}{2}$
The correct answer is:
(d) It moves with a speed of $\frac{1}{2}v$ away from A.
