Four masses are arranged along a circle of radius $1 \mathrm{m}$ as shown in the figure. The center of mass of this system of masses is at

Coordinates of masses arranged can be written as,

$$\begin{gathered} M\left(1, 0\right) \\ 2M\left(0, 1\right) \\ 3M\left(-1, 0\right) \\ 4M\left(0, -1\right) \end{gathered}$$

Therefore, x-coordinate of centre of mass can be written as,

$$\begin{gathered} X_{cm}=\frac{\left(M\times 1\right)+\left(2M\times 0\right)+\left(3M\times -1\right)+\left(4M\times 0\right)}{M+2M+3M+4M} \\ =\frac{-1}{5} \end{gathered}$$

Similarly, y-coordinate can be written as,

$$\begin{gathered} Y_{cm}=\frac{\left(M\times 0\right)+\left(2M\times 1\right)+\left(3M\times 0\right)+\left(4M\times -1\right)}{M+2M+3M+4M} \\ =\frac{-1}{5} \end{gathered}$$

So we can write, position vector of the centre of mass as, $-\frac{1}{5}\hat{\mathrm{i}}-\frac{1}{5}\hat{\mathrm{j}}$