Five masses are placed in a plane as shown in the figure. The coordinates of the centre of mass are nearest to:

In the case of a system of two particles of different masses,the centre of mass lies

$A$ thin rod of length $L$ is placed along the $X$-axis such that one of its ends is at $x = 0$ and the other is at $x = L$. Its linear mass density (mass/length) varies with $x$ as $k(x/L)^n$,where $n$ is any positive number or zero. If the graph of the center of mass $x_{cm}$ versus $n$ is plotted for the rod,which of the following graphs is correct?

Two bodies $A$ and $B$ have masses $M$ and $m$ respectively,where $M > m$,and they are at a distance $d$ apart. Equal forces are applied to each of them so that they approach each other. The position where they hit each other is

Obtain an expression for the position vector of the centre of mass of a system of $n$ particles in two dimensions.

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.