What is a system of particles?

Two semicircular rings of linear mass densities $\lambda$ and $3\lambda$ and of radius $R$ each are joined to form a complete ring. The distance of the center of mass of the complete ring from its geometrical center is

The centre of mass of an extended body on the surface of the earth and its centre of gravity:

The center of mass of a system of particles with masses $1 \, g, 2 \, g$,and $3 \, g$ is at the origin. When a particle of mass $4 \, g$ with position vector $\alpha(\hat{i} + 2\hat{j} + 3\hat{k})$ is added,the center of mass of the system becomes $(1, 2, 3)$. If $\alpha$ is a constant,its value must be:

Mention the position of the centre of mass of a ring,a disc,and spheres.

The coordinates of the center of mass of the triangular lamina shown in the figure are ....... .