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

Three identical metal balls,each of radius $r$,are placed touching each other on a horizontal surface such that an equilateral triangle is formed when the centres of the three balls are joined. The centre of mass of the system is located at:

Three equal masses are placed at $(0,0)$,$(a,0)$,and $\left( \frac{a}{2}, \frac{a\sqrt{3}}{2} \right)$. Find the coordinates of the center of mass.

The centre of mass of a system of two particles divides the distance between them

Two point masses of $1.5 \ g$ and $2.5 \ g$ are placed at a distance of $16 \ cm$ from each other. If the center of mass is at a distance $x$ from the $1.5 \ g$ mass,then $x = \dots \ cm$.

Three identical uniform thin rods each of mass $m$ and length $L$ are arranged in the $XY$ plane as shown in the figure. $A$ fourth uniform thin rod of mass $3m$ is placed as shown in the figure in the $XY$ plane. The value of length of the fourth rod such that the centre of mass of all the four rods lies at the origin is