The centre of mass of a body:

Three masses are placed on the $x-$axis: $300 \, g$ at the origin,$500 \, g$ at $x = 40 \, cm$ and $400 \, g$ at $x = 70 \, cm$. The distance of the centre of mass from the origin is ....... $cm$.

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?

The sum of moments of all the particles in a system about its center of mass is always . . . . . .

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 ....... $\mathring{A}$.

An object comprises a uniform ring of radius $R$ and its uniform chord $AB$ (not necessarily made of the same material) as shown. Which of the following can not be the centre of mass of the object?