$A$ 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

The position of the centre of mass of the uniform plate as shown in the figure is

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 $cm$)

$A$ 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 $-\frac{a}{X}$,find the value of $X$ (to the nearest integer).

$A$ uniform square plate is shown in the figure. Four identical small squares are removed from its corners. Where will the $C.M.$ (Center of Mass) be located after removing all four squares? Give the answer in terms of quadrants and axes.

$A$ circular disc of radius $R$ is cut from a thin metal plate. $A$ hole of radius $R/2$ is cut from this disc such that it touches the rim of the original disc. Find the distance of the center of mass of the remaining part from the center of the original disc.