Sector of a circular plate shown in figure has position of centre of mass at $y_{CM} =$

A uniform thin metal plate of mass $10 \mathrm{~kg}$ with dimensions is shown. The ratio of $x$ and $y$ coordinates of center of mass of plate in $\frac{n}{9}$. The value of $n$ is $\qquad$

The position of the centre of mass of a cube of uniform density will be at

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 a system two particles of masses $m_1=3 \mathrm{~kg}$ and $\mathrm{m}_2=2 \mathrm{~kg}$ are placed at certain distance from each other. The particle of mass $m_1$ is moved towards the center of mass of the system through a distance $2 \mathrm{~cm}$. In order to keep the center of mass of the system at the original position, the particle of mass $\mathrm{m}_2$ should move towards the center of mass by the distance_______.$\mathrm{cm}$.

If the linear density of a rod of length $3m$ varies as $\lambda = 2 + x$, then the position of centre of gravity of the rod is :