A circular disc of diameter d and a square plate of edge d are placed touching each other at the midpoint of an edge of the plate, as shown in the figure. Determine the centre of mass of the combination, assuming the same mass per unit area for both plates.

Step-by-step solution

Let the centre of the circular disc be the origin (0, 0) . Let be the mass per unit area of both plates. The mass of the circular disc is m₁ = ( d 2 )^2 = d^2 4 . The centre of mass of the disc is at x₁ = 0 . The mass of the square plate is m₂ = d^2 . Since the square plate touches the disc at the midpoint of its edge, the distance from the centre of the disc to the centre of the square plate is the sum of the radius of the disc and half the edge length of the square. Thus, the centre of mass of the square plate is