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Q. The centre of mass of a system of two particles divides the distance between them

MHT CETMHT CET 2004System of Particles and Rotational Motion

Solution:

The position of centre of mass of system for n particles is expressed as
$R_{CM}= \frac {\Sigma m_ir_i}{\Sigma m_i}$
or $\Sigma m_ir_i=$constant
Hence, for a system having two particles, we have
$m_1r_1=m_2r_2$
$\Rightarrow \frac {r_1}{r_2}= \frac {m_2}{m_1} $
ie, the centre of mass of a system of two particle divides the distance between them in inverse ratio of masses of particles.