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 equilateral triangle $ABC$ is cut from a thin solid sheet of wood. $D, E$ and $F$ are the midpoints of its sides as shown and $G$ is the centre of the triangle. The moment of inertia of the triangle about an axis passing through $G$ and perpendicular to the plane of the triangle is $I_0$. If the smaller triangle $DEF$ is removed from $ABC$,the moment of inertia of the remaining figure about the same axis is $I$. Then

$A$ square plate of side $12 \ cm$ is shown in the figure. If a square of side $2 \ cm$ is cut from one of its corners,where will the center of mass of the remaining part be with respect to the center of the original square? The plate has uniform thickness and density.

From a circle of radius $a,$ an isosceles right-angled triangle with the hypotenuse as the diameter of the circle is removed. The distance of the centre of gravity of the remaining portion from the centre of the circle is

From a uniform square plate,one-fourth part is removed as shown. The centre of mass of the remaining part will lie on:

$A$ circular plate of uniform thickness has a diameter of $56 \ cm$. $A$ circular part of diameter $42 \ cm$ is removed from one edge. What is the position of the centre of mass of the remaining part in $cm$?