Does the centre of mass of a system of two particles lie on the line joining the two particles?

Define centre of mass of a system of particles.

Determine the co-ordinates of centre of mass of a system of n particles.

Where does the centre of mass of a rectangle lie?

Given that linear momentum of a system of particles is zero.

The centre of mass of a system of particles moves as if all the _________ of the system was concentrated at the _________ of mass and all the external forces acting on the system were applied directly at this point.

Two particles of equal masses m and m are connected by a light string of length 2l. A constant force F is applied continuously at the mid-point of the string, always along the perpendicular bisector of the straight line joining the two particles. Show that when the distance between the two particles is x, the acceleration of the particle is a = F/m = (x)/((1^2 - x^2) ^(1//2)