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Two atoms of oxygen are located at $\mathbf{r}_1$ and $\mathbf{r}_2$. Their centre of mass is at
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Verified Answer
The correct answer is:
$\frac{r_1+r_2}{2}$
Centre of mass of two atoms of oxygen is given as
$$
\begin{aligned}
\mathrm{r}_{\mathrm{CM}} & =\frac{m_1 \mathrm{r}_1+m_2 \mathrm{r}_2}{m_1+m_2}=\frac{m \mathrm{r}_1+m \mathrm{r}_2}{m+m}\left[\because m_1=m_2=m\right] \\
& =\frac{m\left(\mathrm{r}_1+\mathrm{r}_2\right)}{2 m} \\
\mathrm{r}_{\mathrm{CM}} & =\frac{\mathrm{r}_1+\mathrm{r}_2}{2}
\end{aligned}
$$
$$
\begin{aligned}
\mathrm{r}_{\mathrm{CM}} & =\frac{m_1 \mathrm{r}_1+m_2 \mathrm{r}_2}{m_1+m_2}=\frac{m \mathrm{r}_1+m \mathrm{r}_2}{m+m}\left[\because m_1=m_2=m\right] \\
& =\frac{m\left(\mathrm{r}_1+\mathrm{r}_2\right)}{2 m} \\
\mathrm{r}_{\mathrm{CM}} & =\frac{\mathrm{r}_1+\mathrm{r}_2}{2}
\end{aligned}
$$
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