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 equal masses are placed at $(0,0)$,$(a,0)$,and $\left( \frac{a}{2}, \frac{a\sqrt{3}}{2} \right)$. Find the coordinates of the center of mass.

Three identical uniform thin rods each of mass $m$ and length $L$ are arranged in the $XY$ plane as shown in the figure. $A$ fourth uniform thin rod of mass $3m$ is placed as shown in the figure in the $XY$ plane. The value of length of the fourth rod such that the centre of mass of all the four rods lies at the origin is

If the density of the material of a circular plate and a square plate as shown is the same,the center of mass of the composite system will be:

The center of mass of three particles of masses $10 \ kg, 20 \ kg$,and $30 \ kg$ is at $(0, 0, 0)$. Where should a fourth particle of mass $40 \ kg$ be placed so that the center of mass of the system shifts to $(3, 3, 3)$?

Write the meaning of homogeneous bodies.