Explanation

(a) The situation can be shown as
[image:7_image117.emf]
Let radius of complete disc is $a$ and that of small disc is $b$. Also let centre of mass now shifts to $O_{2}$ at a distance $x_{2}$ from original centre.
The position of new centre of mass is given by
$X_{CM} = \frac{- \sigma\pi b^{2}x_{1}}{\sigma\pi a^{2} - \sigma\pi b^{2}}$
Here, $a = 6\ cm,\ b = 2\ cm,\ x_{1} = 3.2\ cm$
Hence, $X_{CM} = \frac{- \sigma \times \pi(2)^{2} \times 3.2}{\sigma \times \pi{\times (6)}^{2} - \sigma \times \pi \times (2)^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = - \frac{12.8\pi}{32\pi} = - 0.4\ cm$