The centre of mass of a homogeneous semi-circular plate of radius $r$ is located at $A$ as shown in the figure. The distance $OA$ is

$A$ uniform square plate is shown in the figure. Four identical squares are removed from its corners. If squares $1$ and $3$ are removed,where will the center of mass $(C.M.)$ be located?

Three identical spheres,each of mass $2 M$,are placed at the corners of a right-angled triangle with mutually perpendicular sides equal to $4 \ m$ each. Taking the point of intersection of these two sides as the origin,the magnitude of the position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$,where the value of $x$ is . . . . . .

On a horizontal frictionless frozen lake,a girl of mass $36 \,kg$ and a box of mass $9 \,kg$ are connected to each other by means of a rope. Initially,they are $20 \,m$ apart. The girl exerts a horizontal force on the box,pulling it towards her. How far has the girl travelled when she meets the box?

Three identical spheres,each of mass $M$,are placed at the corners of a right-angled triangle with mutually perpendicular sides equal to $2 \; m$ (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin,find the position vector of the center of mass.

Choose the correct statement about the centre of mass $(CM)$ of a system of two particles.