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

$A$ disc of mass $M$ with uniform surface mass density $\sigma$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $(\frac{x}{3} \frac{R}{\pi}, \frac{x}{3} \frac{R}{\pi})$,where $R$ is the radius of the disc and $x$ is ....... . (Round off to the nearest integer)

$A$ circular plate of diameter '$a$' is kept in contact with a square plate of side '$a$' as shown. The density of the material and the thickness are same everywhere. The centre of mass of the composite system will be ...........

$A$ circular hole of radius $3 \text{ cm}$ is cut out from a uniform circular disc of radius $6 \text{ cm}$. The centre of the hole is at $3 \text{ cm}$ from the centre of the original disc. The distance of the centre of gravity of the resulting flat body from the centre of the original disc is: (in $\text{ cm}$)

Consider a circular disc of radius $20 \ cm$ with centre located at the origin. $A$ circular hole of radius $5 \ cm$ is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of the centre of mass of the residual or remaining disc from the origin will be (in $cm$)

$A$ thin uniform circular disc has mass $9M$ and radius $R$. $A$ small circular part of radius $R/3$ is cut from the disc as shown in the figure. Calculate the moment of inertia of the remaining part about an axis passing through the center $O$ and perpendicular to the plane of the disc.