Question

In the figure shown, a hole of radius $2\text{cm}$ is made in a semicircular disc of radius $6\pi$ at a distance $8\text{cm}$ from the centre $\text{C}$ of the disc. The distance of the centre of mass of this system from point $\text{C}$ is: (COM of semicircle of radius $r$ is at distance $\frac{4r}{3\pi }$ from the base)

• A. $4\text{cm}$
• B. $8\text{cm}$
• C. $6\text{cm}$
• D. $12\text{cm}$

Answer 1

The correct option is B $8\text{cm}$

Point $\text{C}$ is assumed to be the origin.
We know that:
y coordinate of COM of the half disc
$y_1=\frac{4r}{3\pi }=\frac{4\times 6\pi }{3\pi }=8\text{cm}$
y coordinate of COM of the hole $y_2=8\text{cm}$
which coincides with $y_1$.

So we can see that there is uniform mass removal in all directions w.r.t original COM. So, no change in the position of centre of mass. It will still be $8\text{cm}$.