proof of the property related to center of mass.

Question

Prove the following statement:

"THE SUMMATION OF MASS MOMENTS OF ALL THE COMPONENTS OF SYSTEM ABOUT ITS CENTRE OF MASS IS ALWAYS EQUAL TO ZERO."

Comments

This isn't even true in general, but only holds for systems in rotational equilibrim/when weight is the only force acting.

Anyway, this question is off-topic for PhysicsOverflow as PhysicsOverflow is strictly a graduate-level-only site while this question is high-school or primary-school level.

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Isn't it a definition of the center of mass $\mathbf{R}_{\rm{CM}}=\sum_i m_i\mathbf{r}_i/M_{\rm{tot}}$? When $\mathbf{R}_{\rm{CM}}=0$ it means the sum of mass moments is zero.