Question

what is the formula of centre of mass for discrete objects

Answer 1

In the figure above, we take two particles with masses m1 and m2 respectively lying on the x-axis. The distance of both the particles from the centre O is d1 and d2 respectively. The CoM of this two system of particles is at point C lying at a distance D from point O. In this system of two particles D can be written as:

D = m1d1 + m2d2 / m1 + m2

From the equation D, can be taken as the mass-weighted mean of d1 and d2. Now, let us presume that the particles in the system have equal masses. Hence, m1=m2 = m, in this case,

D = (md1 + md2)/ 2m = m (d1 + d2) / 2m

D = (d1 + d2) / 2

From the equation above we get the centre of mass of two particles with equal masses. From the above equation, it is clear that the CoM of two particles lies in the midway of both.

Centre of Mass for n Particles

For a system of n particles, the centre of mass, according to its definition is:

D = m1d1 + m2d2 + m3d3 +…… mndn / m1 + m2 + m3 +….. mnm = ∑midi / mi

mi here is the sum of the masses of the particles.