Where is the centre of mass of two isolated particles of equal mass located?

If the linear density of a rod of length $3 \ m$ varies as $\lambda = 2 + x$,then the position of the centre of mass of the rod is

$A$ $T$-shaped object is placed on a smooth surface as shown in the figure. $A$ force $\vec{F}$ is applied at point $P$ in a direction parallel to $AB$ such that the object undergoes pure translational motion without rotation. Find the position of point $P$ relative to point $C$.

The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1 Å$. Given,mass of carbon atom is $12 amu$ and mass of oxygen atom is $16 amu$. Calculate the position of the centre of mass of the carbon monoxide molecule.

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

How can a general body be treated in mechanics?