The $(x, y)$ coordinates (in $cm$) of the centre of mass of letter $E$ relative to the origin $O$,whose dimensions are shown in the figure are: (Take width of the letter $2 \ cm$ everywhere).

The figure shows a composite system of two uniform rods of lengths as indicated. The coordinates of the centre of mass of the system of rods are ...........

$A$ disk of radius $R$ is removed from a larger disk of radius $2R$. The circumferences of both disks are tangent to each other. The center of mass of the new disk is at a distance $x$ from the center of the larger disk. Find the value of $x/R$.

$A$ uniform circular disc has radius $r$. $A$ square portion of diagonal $r$ is cut from it. The centre of mass of the remaining disc from the centre of the disc is

In the figure shown,find the distance of the centre of mass of a system of a uniform circular plate of radius $3R$ from $O$,in which a hole of radius $R$ is cut whose centre is at a distance of $2R$ from the centre of the large circular plate.

$A$ 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