Explanation

(a) The situation can be shown as: 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
[image:7_image120.emf]
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, $a = 6cm,\ b = 2cm\ x_{1} = 3.2cm$
Hence, $X_{CM} = \frac{- \sigma \times \pi(2)^{2} \times 3.2}{\sigma \times \pi \times (6)^{2} - \sigma \times \pi \times (2)^{2}}$
$= \frac{12.8\pi}{32\pi} = - 0.4cm$