Question

Three particles each 1kgmass are placed at the corners of a right angled triangle AOB, O being the origin of the coordinate system (OA OB) along positive x direction and positive y-direction.The position vector of the centre of mass? if OA=OB=1mt(in meters)

Answer 1

$$\begin{gathered} A\equiv \left(1,0\right) \\ and \\ B\equiv (0,1) \end{gathered}$$
$$\begin{gathered} \left(x_{cm},y_{cm}\right)=\left(\frac{1\times 0+1\times 1+1\times 0}{3},\frac{1\times 0+1\times 0+1\times 1}{}\right) \\ \Rightarrow \left(x_{cm},y_{cm}\right)=\left(\frac{1}{3},\frac{1}{3}\right) \end{gathered}$$
Position vector of the COM is, $\frac{1}{3}\hat{i}+\frac{1}{3}\hat{j}$