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

Four identical particles each of mass $m$ are kept at the four corners of a square of side $a$. If one of the particles is removed,the shift in the position of the centre of mass 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

The centre of mass of two particles lies:

In the $HCl$ molecule,the separation between the nuclei of the two atoms is about $1.27 \, \mathring{A}$ $(1 \, \mathring{A} = 10^{-10} \, m)$. The approximate location of the centre of mass of the molecule from the hydrogen atom,assuming the chlorine atom to be about $35.5$ times as massive as the hydrogen atom,is ....... $\mathring{A}$.

The balls $A, B$ and $C$ of masses $50 \ g, 100 \ g$ and $150 \ g$,respectively,are placed at the vertices of an equilateral triangle. The length of each side is $1 \ m$. If $A$ is placed at $(0,0)$ and $B$ is placed at $(1,0) \ m$,find the coordinates $(x, y)$ for the centre of mass of this system of the balls.