Show that a system of particles moving under the influence of an external force, moves as if the force is applied at its centre of mass.

The path of a particle moving under the influence of a force fixed in magnitude and direction is [

If the external forces acting on a system have zero resultant, the centre of mass

If the external forces acting on a system have zero resultant, the centre of mass

If the external forces acting on a system have zero resultant, the centre of mass

Show that the total linear momentum of a system of particles is conserved in the absence of any external force. Also show that total linear momentum of the system is equal to the product of the total mass of the system and the velocity of its centre of mass.

A system of particles is free from any external force vec v and vec a be the velocity and acceleration of the centre of mass, then it necessarily follows that :