Let's find out the centre of mass for carbon monoxide, useful for the Olympiad.
The Problem:
Find the centre of mass of a CO molecule.
Solution:
Let the centre of mass be located at a distance (r_c) from the carbon atom and at (r_0) from the oxygen atom along the line joining the carbon and oxygen atoms.
$$ m_cr_c=m_or_o=m(r-r_c)$$
$$ r_c =\frac{m_or}{m_o+m_o}=\frac{16\times1.13}{12+16}=0.646 Angstrom$$
