$A$ system consists of $3$ particles each of mass $m$ located at $(1, 1), (2, 2),$ and $(3, 3)$. The coordinates of the centre of mass are

Three identical spheres,each of mass $M$,are placed at the corners of a right-angled triangle with mutually perpendicular sides equal to $2 \; m$ (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin,find the position vector of the center of mass.

Two identical uniform rectangular blocks (with longest side $L$) and a solid sphere of radius $R$ are to be balanced at the edge of a heavy table such that the centre of the sphere remains at the maximum possible horizontal distance from the vertical edge of the table without toppling as indicated in the figure. If the mass of each block is $M$ and of the sphere is $M/2$,then the maximum distance $x$ that can be achieved is

Mass is distributed uniformly over a thin square plate. If two end points of a diagonal are $(-2, 0)$ and $(2, 2)$,what are the coordinates of the centre of mass of the plate?

$A$ rod of length $5L$ is bent at a right angle,keeping one side length as $2L$. Find the position of the center of mass of the system. (Consider $L = 10 \ cm$)

Mass is distributed uniformly over a thin rectangular plate,and the positions of two vertices are given by $(1, 3)$ and $(2, -4)$. What is the position of the $3^{rd}$ vertex if the centre of mass of the plate lies at the origin?