$A$ 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 $cm$?

$A$ smaller cube with side $b$ (depicted by dashed lines) is excised from a bigger uniform cube with side $a$ as shown below,such that both cubes have a common vertex $P$. Let $X = a/b$. If the centre of mass of the remaining solid is at the vertex $O$ of the smaller cube,then $X$ satisfies:

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

The coordinates of the centre of mass of a uniform $L$-shaped plate of mass $3 \ kg$ shown in the figure is:

The figure shows a uniform square plate from which four identical small squares have been removed from the corners. If square $1$ is removed,where will the center of mass $(C.M.)$ be located?

For the given uniform square lamina $ABCD$ whose centre is $O$,pick the incorrect statement.