The centre of mass of a body

Two particles of masses $5 \,g$ and $3 \,g$ are separated by a distance of $40 \,cm$. The centre of mass of the system of these two particles

Define the position vector of the centre of mass.

When two masses $m$ and $M$ $(M > m)$ are connected,where will the center of mass be located?

Give two examples of rigid bodies whose center of mass lies outside the material of the body.

$A$ $T$-shaped object with dimensions shown in the figure is lying on a smooth floor. $A$ force $\vec{F}$ is applied at point $P$ parallel to $AB$,such that the object has only translational motion without rotation. Find the location of $P$ with respect to $C$.