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?

When two masses $m$ and $M$ $(M > m)$ are connected,where will the center of mass be located?

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?

Masses $m, (1/2)(m/2), (1/2)^2(m/3), \dots, (1/2)^{N-1}(m/N), \dots \infty$ are placed at $x = 1, 2, 3, \dots, N, \dots \infty$ respectively. If the total mass is $M$,then the centre of mass of the system is:

Two point masses $M$ each are placed at $(L, 0)$ and $(-L, 0)$. $A$ third point mass $M$ is uniformly rotating on the circle $x^2 + y^2 = L^2$. The equation of the path traced by the $COM$ of the $3$ point masses is:

Weights of $1\,g, 2\,g, \dots, 100\,g$ are suspended from the $1\,cm, 2\,cm, \dots, 100\,cm$ marks respectively of a light metre scale. Where should it be supported for the system to be in equilibrium?