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?

Three particles of masses $1\,kg$,$\frac{3}{2}\,kg$,and $2\,kg$ are located at the vertices of an equilateral triangle of side $a$. The $x, y$ coordinates of the centre of mass are

Each side of a rhombus has length $a$. Four particles of masses $m, 2m, 3m$ and $4m$ are placed at the vertices of the rhombus. The angle between two adjacent sides of the rhombus is $60^o$. The rhombus lies in the $x-y$ plane,with mass $m$ at the origin and mass $4m$ on the $x$-axis. Find the coordinates of the center of mass of this system.

$A$ square plate and a circular disc of uniform density are arranged as shown in the figure. The center of mass of this combined system will be .........

If two bodies of masses $2 \,kg$ and $3 \,kg$ are moving at right angles with velocities $20 \,m \,s^{-1}$ and $10 \,m \,s^{-1}$ respectively, then the velocity of the centre of mass of the system of the two bodies is

Three bodies each of mass $1 \,kg$ are situated at the vertices of an equilateral triangle of side $1 \,m$. The $x y$-coordinates of the centre of mass of the system are: