$A$ circular plate of uniform thickness with a diameter of $56\, cm$ has its center at the origin. $A$ circular part with a diameter of $42\, cm$ is removed from one edge. What is the distance of the center of mass of the remaining part in $cm$?

$A$ 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:

$A$ circular disc of radius $R$ is removed from one end of a bigger circular disc of radius $2R$. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

$A$ uniform square plate of side $a$ has a circular hole of diameter $a/2$ cut out from it as shown in the figure. The center of the hole is at $a/4$ from the center of the square plate. The distance of the center of mass of the resulting plate from the center of the square is:

$A$ solid cone is placed on a horizontal surface has height $h$,radius $R$ and apex angle $\theta$ as shown. If the gravitational potential energy of the cone does not change as the position of the cone is changed from figure $(A)$ to figure $(B)$,then,

$A$ regular square plate is shown in the figure. Four identical squares are removed from its corners. Where will the $C.M.$ (Centre of Mass) be located if squares $1$ and $2$ are removed?