A system consists of $3$  particles each of mass $m$ and located at $(1, 1), (2, 2), (3, 3)$. The co-ordinate of the centre of mass are

The distance of centre of mass from end $A$ of a one dimensional rod $( AB )$ having mass density $\rho=\rho_{0}\left(1-\frac{ x ^{2}}{ L ^{2}}\right)\,kg / m$ and length $L$ (in meter) is $\frac{3 L }{\alpha} m$. The value of $\alpha$ is $\ldots \ldots \ldots . .$ (where $x$ is the distance form end $A$ )

A square shaped hole of side $l=\frac{a}{2}$ is carved out at a distance $d =\frac{ a }{2}$ from the centre $'O'$ of a uniform circular disk of radius $a$. If the distance of the centre of mass of the remaining portion from $O$ is $-\frac{a}{X},$ value of $X$ (to the nearest integer) is.......

In the figure shown find out the distance of centre of mass of a system of a uniform circular plate of radius $3R$ from $O$ in which a hole of radius $R$ is cut whose centre is at $2R$ distance from centre of large circular plate

A small disc of radius $2\, cm$ is cut from a disc of radius $6\, cm$. If the distance between their centres is $3.2\, cm$, what is the shift in the centre of mass of the disc ....... $cm$.

Mention the position of centre of mass of particles of equal mass.