Four particles of masses $1\,kg, 2 \,kg, 3 \,kg$ and $4\, kg$ are placed at the four vertices $A, B, C$ and $D$ of a square of side $1\, m$ as shown in the figure. The coordinates of the centre of mass of the particles are:

Three identical spheres,each of mass $1 \ kg$,are arranged as shown in the figure. If their centers of mass are at $P$,$Q$,and $R$ respectively,what is the distance of the center of mass of this system from point $P$?

The centre of mass of a non-uniform rod of length $L$ whose mass per unit length $\lambda$ varies as $\lambda = \frac{k x^3}{L^3}$ (where $k$ is a constant and $x$ is the distance of any point on the rod from one end) is at a distance from the same end equal to:

Two particles of masses $m_1$ and $m_2$ are separated by a distance $d$. The distance of the centre of mass of the system from the particle of mass $m_1$ is:

Consider the following statements regarding the Centre of Mass $(CM)$ of objects of radius $R$ from their geometric centre:
$[1]$ $CM$ of a uniform semicircular disc is at $2R/\pi$.
$[2]$ $CM$ of a uniform semicircular ring is at $4R/3\pi$.
$[3]$ $CM$ of a solid hemisphere is at $4R/3\pi$.
$[4]$ $CM$ of a hemispherical shell is at $R/2$.
Which of these statements are correct?

Particles of masses $8 \, kg, 2 \, kg, 4 \, kg$,and $2 \, kg$ are placed at the vertices $A, B, C$,and $D$ of a square respectively. The distance of the center of mass of the system from vertex $A$ is $....... \, cm$. The length of the diagonal of the square is $80 \, cm$.