Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be

Let us determine the center of mass’s speed as it moves toward one another due to their mutual attraction since two particles initially are at rest. We may regard the individual speeds of the particles as they move toward each other. One of them is moving at a speed v, and the other at the speed 2v.

In the initial state, both particles are at rest and therefore have zero initial momentum. As they start moving toward one another, acceleration occurs due to the mutual gravitational attraction between the particles. The velocity of the center of mass is the main concept in this scenario, representing the overall motion of the system based on individual masses and their respective velocities.

Despite the fact that the particles are accelerating as they approach each other, the principle of conservation of momentum states that the center of mass is unchanged. The relative motion of the two particles will affect the center of mass, and since they are moving toward each other, the center of mass remains stationary. Thus, the effect of their combined motion is to produce no overall acceleration in the center of mass. Therefore, the speed of the center of mass of this system is zero, meaning that the motion of the individual particles does not alter the overall state of rest of the system.

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