Answer
$.1r$
Work Step by Step
We know that a point on a circle is given by $rsin\theta$. We know that this semi-circle ranges from $\theta = 0$ to $\theta=180$. However, we are looking for the y-center of mass, so $\theta$ ranges from $\theta = 45$ to $\theta=135$.
$=\int_0^{180}rsin\theta d\theta=r\frac{2}{\sqrt{2}}$
We use this to find the center of mass:
$y_{cm}=1-\frac{\sqrt2 r}{1}\times\frac{2}{\pi}=.1r$
