$x_{cm} = 0$ because of symmetry of the arc about the $y-$axis

$y_{cm} = \cfrac{\int y dm}{\int dm}$
$=\cfrac{R^2 \int_{\cfrac{\pi -\alpha}{2}}^{\cfrac{\pi + \alpha}{2}} \sin \theta}{R \int_{\cfrac{\pi -\alpha}{2}}^{\cfrac{\pi + \alpha}{2}} \theta}$
$=\cfrac{R \sin (\alpha/2)}{(\alpha / 2)}$

Center of Mass of Circular Ring

Coordinates of center of mass of semicircular ring are:
$x_{cm} = 0$
$y_{cm} = \cfrac{R \sin (\pi / 2)}{(\pi / 2)}$ $=\cfrac{2R}{\pi}$ (Refer the center of mass of arc)