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 $\qquad$

From a circular disc of radius $R$ a triangular portion is cut (see fig.). The distance of  $COM$ of the remaining disc from centre of disc $O$ is:-

From a uniform disk of radius $R$, a circular hole of radius $R/2$ is cut out. The centre of the hole is at $R/2$ from the centre of the original disc. Locate the centre of gravity of the resulting flat body.

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass $4\;kg$. (The coordinates of the same are shown in figure) are

A smaller cube with side $b$ (depicted by dashed lines) is excised from a bigger uniform cube with side $\alpha$ as shown below, such that both cubes have a common vertex $P$. Let $X=a / b$. If the centre of mass of the remaining solid is at the vertex $O$ of smaller cube, then $X$ satisfies

A rod of length $3\, m$ and its mass per unit length is directly proportional to the distance $x$ from its one end. The center of gravity of the rod from that end will be at ........ $ m$