$m_{1}$ and $m_{2}$ are two bodies of masses separated by a distance $R$. The distance of the centre of mass of the bodies from the mass $m_{1}$ is

Centre of mass $(C.M.)$ of three particles of masses $1 \,kg, 2 \,kg$ and $3 \,kg$ lies at the point $(1, 2, 3)$ and $C.M.$ of another system of particles of $3 \,kg$ and $2 \,kg$ lies at the point $(-1, 3, -2)$. Where should we put a particle of mass $5 \,kg$ so that the $C.M.$ of the entire system lies at the $C.M.$ of the first system?

Find the $x$ coordinate of the centre of mass of the books shown in the figure. Every book has mass $m$.

Explain the theoretical method for the estimation of the centre of mass of a solid body.

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

The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1 \ \mathring{A}$. Given,mass of carbon atom is $12 \ a.m.u.$ and mass of oxygen atom is $16 \ a.m.u.$,calculate the position of the center of mass of the carbon monoxide molecule.