pls explain m1r1= m2r2...

Dear Student!

Consider Vector r₁ and r₂ are position vector of particle of mass m₁ and m₂.

Vector R is the position vector of the center of mass of the two particle system.

$\vec{R} = \frac{m_{1 \vec{r_{1}} + m_{2} \vec{r_{2}}}}{m_{1} + m_{2}}$

Consider that center of mass lie at the origin.

Then vector r₁ and r₂ lie on the opposite side of the origin.

$\vec{R} = 0 = \frac{m_{1 \vec{r_{1}} + m_{2 (-} \vec{r_{2}})}}{m_{1} + m_{2}} m_{1 \vec{r_{1}} - m_{2} \vec{r_{2}}} = 0 m_{1 \vec{r_{1}} = m_{2} \vec{r_{2}}}$

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