A small disc of radius 2 cm is cut from a disc of radius 6 cm . If...

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 $\mathrm{O}_2$ at a distance $x_2$ from original centre. The position of new centre of mass is given by $X_{\mathrm{CM}}=\frac{-\sigma \cdot \pi b^2 \cdot x_1}{\sigma \cdot \pi a^2-\sigma \cdot \pi b^2}$ Here, $a=6 \mathrm{~cm}, b=2 \mathrm{~cm}, x_1=3.2 \mathrm{~cm}$ Hence, $\quad X_{\mathrm{CM}}=\frac{-\sigma \times \pi(2)^2 \times 3.2}{\sigma \times \pi \times(6)^2-\sigma \times \pi \times(2)^2}$$\begin{aligned} & =\frac{12.8 \pi}{32 \pi} \\ & =-0.4 \mathrm{~cm}\end{aligned}$$$