Let origin be the centre of mass of the body which is represented by C. i.e. r=0 ∴ From Eq. (i), we get m1r1+m2r2+m1r3+...mnrn=0 ...(ii) Net moment of all particles in the system about centre of mass C. τC=m1gr1+m2gr2+m3gr3+...mngrn =g[m1r1+m2r2+m3r3+...+mnrn] =g×0 [from Eq. (ii)] = 0 Hence, sum of moments of all the particles in a system about its centre of mass is always zero.
