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

Infinite rods of uniform mass density and lengths $L, L/2, L/4, \dots$ are placed one upon another up to infinity as shown in the figure. Find the $x-$ coordinate of the centre of mass.

What do you mean by mass element $dm$?

Look at the figure drawn with ink of uniform linear density. $A$ mass $m$ of ink is used to draw each of the two inner circles and each of the two line segments. $A$ mass $6m$ of ink is used to draw the outer circle. The coordinates of the centers of the different parts are: outer circle $(0, 0)$,left inner circle $(-a, a)$,right inner circle $(a, a)$,and the horizontal line segment $(0, -a)$. Find the $y$-coordinate of the center of mass of the ink in the figure.

In the figure shown,$ABC$ is a uniform wire. If the center of mass of the wire lies vertically below point $A$,then $\frac{BC}{AB}$ is close to:

Three particles of mass $1 \ kg, 2 \ kg$ and $3 \ kg$ are placed at the vertices $A, B$ and $C$ respectively of an equilateral triangle $ABC$ of side $1 \ m$. The centre of mass of the system from vertex $A$ (located at origin) is