In the case of a system of two particles of different masses,the centre of mass lies

$A$ uniform square wooden sheet of side $a$ has its centre of mass located at its geometric centre. $A$ square portion of side $b$ is cut out from one corner to produce an $L$-shaped sheet. The centre of mass of the $L$-shaped sheet lies at the inner corner point $P$ of the cut-out, when:

The centre of mass of a body

In the $HCl$ molecule,the separation between the nuclei of the two atoms is about $1.27 \; \mathring{A} \; (1 \; \mathring{A} = 10^{-10} \; m)$. Find the approximate location of the center of mass $(CM)$ of the molecule,given that a chlorine atom is about $35.5$ times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

$A$ thin rod of length $L$ is placed along the $X$-axis such that one of its ends is at $x = 0$ and the other is at $x = L$. Its linear mass density (mass/length) varies with $x$ as $k(x/L)^n$,where $n$ is any positive number or zero. If the graph of the center of mass $x_{cm}$ versus $n$ is plotted for the rod,which of the following graphs is correct?

Obtain the general expression for the centre of mass of a system of $n$ distributed particles in three dimensions.