AIIMS 2018 Physics Center of Mass MCQ Question

The distance of the center of mass of a half ring from its center is given by the formula $\frac{R}{2} \cdot \frac{1}{\pi}$, where $R$ is the radius of the ring. For a half ring with a radius of 0.5 m, this calculates to $\frac{0.5}{2} \cdot \frac{1}{\pi} = \frac{1}{4\pi}$, which simplifies to $\frac{1}{\pi}$ when considering the full distance from the center. Other options are incorrect as they do not accurately represent the derived formula for the center of mass of a half ring, which specifically depends on the geometry of the shape and its uniform mass distribution.