From a circular disc of radius R , a square is cut out with a radius as its diagonal. The centre of mass of remaining portion is at a distance (from the centre)

Step-by-step solution

Let the radius of the circular disc be R . The area of the disc is A₁ = R^2 . The centre of mass of the disc is at the origin (0, 0) . A square is cut out such that its diagonal is equal to the radius R . Let the side of the square be a . Then, a 2 = R , which implies a = R 2 . The area of the square is A₂ = a^2 = R^2 2 . The centre of mass of the square is at the centre of the disc (0, 0) . However, the problem implies the square is cut from the disc such that its diagonal lies along a radius. Let the centre of th