The distance of centre of mass of a uniform semicircular disc of radius R, from the geometric center on the axis of symmetry is

Explanation

The `y-`axis is the line of symmetry, therefore mass center of the ring lies on it making x-cordinate zero. Distance OC of mass center from center is given by the result obtained in example 4. Making use of this result, we have
`OC = (r sin theta)/(theta)rarr y_(c ) = (r sin (pi //2))/(pi//2) = (2pi)/(pi)`