Question

What is the significance of the centre of
mass of an N-particle system ? Locate the
centre of mass of a system of 4 particles
shown below with respect to the particle of
mass m

Answer 1

Significance of the centre of mass of N particles is the point in space where mass of the whole rigid body is located. Centre of mass of N particles is the vector sum of the moment of the masses, of individual particles around the reference point divided by total mass of the rigid body.

Let, 4-particles of mass m located in the corner of a square, then centre of mass will be the point of intersection of its diagonals.