The center of gravity of a semicircle lies at a distance of _______ from its base measured along the vertical radius.

Correct option is C

The center of gravity (centroid) of a semicircle of radius (r) is located at a distance of 4r/3π from the flat (base) side along the vertical radius. This distance is derived from the geometric properties of a semicircle and is a fundamental result in statics and mechanics of materials.
Thus, the correct distance of the center of gravity from the base of a semicircle is 4r/3π.