An object comprises of a uniform ring of radius R and its uniform chord AB (not necessarily made of the same material) as shown. Which of the following cannot be the centre of mass of the object?

The centre of mass of the object must lie on the line segment joining (0, 0) and . (R/2, R/2). Co-ordinates of centre of mass of rod are (R/2, R/2) and Co-ordinates of centre of mass of ring are (0, 0). So the centre of mass of the object must lie on the line joining (0, 0) and . (R/2, R/2). Hence xc < R/2 and yc < R/2. Since R/√2 > R/2, option (2) is right.