Question

In the figure shown a hole of radius $2cm$ is made in a semicircular disc of radius $6\pi$ at a distance $8cm$ from the centre $C$ of the disc. The distance of the centre of mass of ths system from point $C$ is:

• A. $4cm$
• B. $8cm$
• C. $6cm$
• D. $12cm$

Answer 1

The correct option is B $8cm$

$y_{cm}=\frac{4r}{3\pi }$ (for half disc)

$y_{cm}=\frac{4\times 6\pi }{3\pi }=8cm$

And also we see that a disk is removed from that point 8 cm as a centre. So, there is uniform mass removal in all direction so no change in the position of centre of mass. It will still be $8cm.$