Find the center of mass $(x, y, z)$ of the following structure of four identical cubes if the length of each side of a cube is $1$ unit.

Four bodies of equal mass start moving with the same speed as shown in the figure. In which of the following combinations will the centre of mass remain at the origin?

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?

$A$ $T$-shaped object of uniform thickness and same material with dimensions shown in the figure,is lying on a smooth floor. $A$ force $\vec F$ is applied at the point $P$ parallel to $AB$,such that the object has only the translation motion without rotation. Find the location of $P$ with respect to $C$.

In the $HCl$ molecule,the separation between the nuclei of the two atoms is about $1.27 \, \mathring{A}$ $(1 \, \mathring{A} = 10^{-10} \, m)$. The approximate location of the centre of mass of the molecule from the hydrogen atom,assuming the chlorine atom to be about $35.5$ times as massive as the hydrogen atom,is ....... $\mathring{A}$.

Two objects $A$ and $B$ of masses $M$ and $m$ respectively,where $M > m$,are separated by a distance. They move towards each other under the influence of equal forces. At what point will they collide?