The center of mass (COM) of a uniform circular sector is along its axis of symmetry. Its distance from the center O is calculated by integrating the position of infinitesimal mass elements over the entire sector.

The formula for the y-coordinate of the COM is derived as:

$y=\frac{2R\sin \left(\frac{{\theta }_0}{2}\right)}{3{\theta }_0}$

This result is obtained because the mass is distributed symmetrically about the x-axis, making the x-coordinate zero. The correct option is the one that matches this derived formula.

Final Answer: $\frac{2R\sin \left(\frac{{\theta }_0}{2}\right)}{3{\theta }_0}$