Solution
= Solution
For an axis through the <center of mass> perpendicular to the bond, the point-mass <moment of inertia> is
$$
\begin{aligned}
I&=m_{\rm C}r_1^2+m_{\rm S}r_2^2\\
&=\frac{m_{\rm C}m_{\rm S}^2+m_{\rm S}m_{\rm C}^2}
{(m_{\rm C}+m_{\rm S})^2}r^2
=\boxed{\frac{m_{\rm C}m_{\rm S}}{m_{\rm C}+m_{\rm S}}r^2}.
\end{aligned}
$$
The prefactor is the <reduced mass> $\mu$; this is the standard reduction of a two-body <linear rigid rotor> to $I=\mu r^2$.