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 plate lies on it making x-cordinate zero. Distance OC of mass center from center is given by the result obtained in example 7. Making use of this result, we have
`OC = (r2r sin theta)/(3 theta)rarr y_(c ) = (2r sin (pi//2))/(3pi//2) = (4r)/(3r)`