The disc of mass with uniform surface mass density is shown in the figure. The center of mass of the quarter disc (the shaded area) is at the position where is . (Round off to the Nearest Integer)

Question

The disc of mass  with uniform surface mass density  is shown in the figure. The center of mass of the quarter disc (the shaded area) is at the position  where  is . (Round off to the Nearest Integer) [ is an area as shown in the figure]

Canvas Classes · Accepted Answer

🧠 Quarter Disc — Project the Half-Disc Result onto Both Axes

Read the question. A quarter disc of radius  sits in the first quadrant with its corner at the origin. The figure marks  as the radius (the diagonal line from origin to rim). We need the CM coordinates, given in the form .

The key insight is that the quarter disc is symmetric about the line . So . The CM must sit on the diagonal.

For a quarter disc with corner at origin and rim in the first quadrant, the standard result is

The f

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