Half of the rectangular plate shown in figure is made of a material of density p1 and the other half of density p2. The length of the plate is L. Locate the centre of mass of the plate.
The centre of mass of each half is located at the geometrical centre of that half. Thus, the left half may
be replaced by a point particle of mass Kp1 placed at C1 and the right half may be replaced by a point
particle of mass Kp2 placed at C2. This replacement is for the specific purpose of locating the combined
centre of mass. Take the middle point of the left edge to be the origin. The x-coordinate of C1 is L4 and
that of C2 is 3L4. Hence, the x-coordinate of the centre of mass is
x = (Kp1)L4 + (Kp2)3L4Kp1 + Kp2
= (p1 + 3p2)4(p1 + p2)L.
The combined centre of mass is this much to the right of the assumed origin.