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

Two particles, A and B, start from rest, moving toward each other under mutual forces of attraction. In this case, the center of mass of the system continues to have zero speed. This is so because the system of two particles is isolated; no external forces are acting on it. In such systems, the motion of the center of mass is determined only by external forces. Since there are none in this case, the center of mass remains stationary or maintains a constant velocity. Initially, both particles are at rest, so the velocity of the center of mass is zero.

As they move toward each other because of mutual attraction, their velocities change, but these changes are such that the internal forces do not affect the center of mass. Internal forces always act in equal and opposite directions, thus canceling out their effects on the system as a whole. Hence, even in the case of particle A travelling at speed v and particle B traveling at twice that speed (2v) the center of mass of this system does not gain any velocity to move. Such a scenario is in fact an exercise in the fundamental conservation of momentum concept in isolated systems.

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