Two atoms of oxygen are located at $\mathbf{r}_1$ and $\mathbf{r}_2$. Their centre of mass is at

Two atoms of oxygen are located at $\mathbf{r}_1$ and $\mathbf{r}_2$. Their centre of mass is at
  1. $r_1+r_2$
  2. $\frac{r_1-r_2}{2}$
  3. $\frac{r_1+r_2}{2}$
  4. $r_1-r_2$

Solution

Centre of mass of two atoms of oxygen is given as $ \begin{aligned} \mathrm{r}_{\mathrm{CM}} & =\frac{m_1 \mathrm{r}_1+m_2 \mathrm{r}_2}{m_1+m_2}=\frac{m \mathrm{r}_1+m \mathrm{r}_2}{m+m}\left[\because m_1=m_2=m\right] \\ & =\frac{m\left(\mathrm{r}_1+\mathrm{r}_2\right)}{2 m} \\ \mathrm{r}_{\mathrm{CM}} & =\frac{\mathrm{r}_1+\mathrm{r}_2}{2} \end{aligned} $

Asked in: AP EAMCET 2020 (22 Sep Shift 1)

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