# A circular ring of mass 6 kg and radius a is placed such that its centre lies at the origin.two particles of masses 2 kg each are placed at the intersecting points of the circle with positive x and y axis.find angle made by position vector of centre of mass of entire system

$\begin{array}{l} x_{com}=\frac{2a+0+0}{2+2+6} \\ x_{com}=\frac{2 a}{10}=\frac{a}{5} \\ y_{com}=\frac{0+2 a+0}{2+2+6} \\ x_{com}=\frac{a}{5} \end{array}$

$\begin{array}{l} \tan \theta=\frac{y_{co m}}{x_{c om}} \\ \tan \theta=\frac{a/5}{a / 5} \\ \tan \theta=1 \\ \tan \theta=\tan 45^{\circ} \\ \theta=45^{\circ} \end{array}$

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