Two objects of mass $10\,kg$ and $20\,kg$ respectively are connected to the two ends of a rigid rod of length $10\,m$ with negligible mass. The distance of the center of mass of the system from the $10\,kg$ mass is:

$A$ uniform square plate is shown in the figure. Four identical squares are removed from its corners. If squares $1$ and $3$ are removed,where will the center of mass $(C.M.)$ be located?

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

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.

Find the position of the center of mass of a system of two particles of masses $m_1$ and $m_2$ separated by a distance $L$.

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