Question

Two particles A and B initially at rest move towards each other under a mutual attraction. At the instant when velocity of A is ‘v’ and that of B is ‘2v’, the velocity of center of mass of the system
(A) v
(B) 2v
(C) 3v
(D) Zero

Answer 1

In this question, we need to determine the velocity of the center of the mass of the system such that the velocity of A is ‘v’ and the velocity of B is ‘2v’. For this, we will follow the relation between the momentum, mass and velocity of the particle.

Complete step by step answer:
As the two particles are initially at rest i.e. the initial velocity is zero and consequently the momentum is also zero and because there is no external force involved there will be no change in momentum of the center of mass and it will remain zero.
The product of the mass and the velocity of the particle results in the momentum of the particle. Mathematically, $M = m \times v$ where M is the momentum, ‘m’ is the mass of the particle and ‘v’ is the velocity of the particle.If momentum is zero and mass cannot be zero then the velocity must be zero.Hence, we can say that the velocity of the center of the mass of the system such that the velocity of A is ‘v’ and the velocity of B is ‘2v’ is zero.
Hence,option D is correct.

Note: If the two bodies are attracted mutually without any external force they will always meet at the center of mass of the system no matter what is the mass and velocity of the bodies. No external force implies that there is no change in center of mass of the system.