For a system consisting of two objects,when can they be treated as point particles?

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

The linear mass density of a rod of length $L$ varies as $\lambda = A + Bx$. Find the center of mass.

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.

Masses $8\,kg, 2\,kg, 4\,kg, 2\,kg$ are placed at the corners $A, B, C, D$ respectively of a square $ABCD$ of diagonal $80\,cm$. The distance of the centre of mass from $A$ will be ........ $cm$.

$A$ $T$-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 $C$.