Four identical spheres each of mass $m$ are placed at the corners of a square of side $2 \, m$. Taking the point of intersection of the diagonals as the origin,the coordinates of the centre of mass are

Two bodies of mass $1\,kg$ and $3\,kg$ have position vectors $\hat{i}+2\hat{j}+\hat{k}$ and $-3\hat{i}-2\hat{j}+\hat{k}$ respectively. The magnitude of the position vector of the centre of mass of this system will be equal to the magnitude of which of the following vectors?

When does a body (system) have different centre of gravity and centre of mass?

Define the centre of mass.

Three particles of mass $1 \ kg, 2 \ kg$ and $3 \ kg$ are placed at the vertices $A, B$ and $C$ respectively of an equilateral triangle $ABC$ of side $1 \ m$. The centre of mass of the system from vertex $A$ (located at origin) is

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