Why do the algebraic sum of moment of masses of various particles of a system about its centre of mass is zero? Share with your friends Share 1 Bakul Biswas answered this Dear Student , here in this case , Consider a spherical case of equillibrium of a body acted upon a number of coplanar parallel forces acting on a body .Using the condition number one , i.e. the algebraic sum of the forces acting on a body is zero .Therefore , P+Q+R+S=0Now look if the algebraic sum of the torques or mo0ments of the force about any point in their plane must be zero .So , Clockwise moment=anti clockwise momentEquating moments about point A ,⇒P×AD+Q×AF=R×AC+S×AE⇒P×AD+Q×AF-R×AC-S×AE=0Thus the algebraic sum of the moments of the forces acting on a body about any point is zero .Thus in this way we can say that the algebraic sum of the moments of the masses of various particles in a system about its centre of mass is zero . Regards 1 View Full Answer