Question

Figure shows a uniform disc of radius $R$ from which a hole of radius $R/2$ has been cut out from centre and filled with a material of twice the density of the original disc. Find the change in position of $COM$.

• A. $COM$ will shift $R/2$ distance towards right
• B. $COM$ will shift $R/2$ towards left
• C. $COM$ will shift $2R/3$ distance towards right
• D. Position of $COM$ will not change

Answer 1

The correct option is D Position of $COM$ will not change

Initial coordinates of $COM$ of the disc are $(0,0)$. When the hole is cut out and filled with material of twice the density, the coordinates of $COM$ of hole and the new material are both $(0,0)$
Therefore, coordinates of resulting disc will not change as coordinates of $COM$ of both (hole and new disc) are at the same point $(0,0)$.
Hence, $COM$ of the resulting disc will be at origin $(0,0)$