Question

Two particles A and B initially at rest move towards each other under a mutual force of attraction. The speed of centre of mass at instant when speed of A is v and the speed of B is2v is

Answer 1

Answer:

Zero.

Since no external forces act on the system, the center of mass keeps moving just as it did before the two objects started to exert forces on each other. Since the objects were at rest, they center of mass will remain at the same place. If the two objects are simple spheres or can be thought of as point-like, they will collide at their center of mass.

This is an example of conservation of momentum. Since the system had zero net momentum to begin with and no external forces act on the system, the momentum must be zero at the end.

Knowing that the forces on each object must be equal and opposite, we can deduce from their velocities the relation between their masses. Object A must have twice the mass of Object B.

Answer 2

Answer:

The velocity of centre of mass is zero.

Explanation:

Two particles A and B initially were kept at rest. This means that their centre of mass lies some where between them at half distance.

Now, it is said that they move towards each other under a mutual force of attraction which signifies that A and B constitute a single system. So, the motion of A and B towards each other is internal force here. Hence, the external force acting on the system is zero which implies that the momentum of centre of mass is zero which in turn means that velocity is zero.

Then, since the initial momentum of the body was zero, the final momentum must be zero since the centre of mass of momentum remains constant. Hence, the final velocity is also zero.

Hope it helps! ;-))