Prove that the magnitude of R of the position vector for the centre of mass from an arbitrary origin is given by the equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]M^2R^2 = M\sum m_ir_i^2 - {1\over 2}\sum m_i m_j r_{ij}^2[/tex]

Well the centre of mass is given by:

[tex]\vec R = \frac{\sum m_i r_i}{M}[/tex]

But squaring this doesn't seem to produce the result I require. I need more help.

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# Centre of mass problem

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