A circular plate of uniform thickness has a radius of 14 cm. A circular portion of diameter 21 cm is removed from one edge from the plate as shown in the figure. If ‘O’ is the centre of mass of the complete plate, then the distance of centre of mass of the remaining portion from ‘O’ is
 

C₁ is the center of mass of cut portion and C₂ that of remaining portion. We have to find x₂.

$x_1=14-10.5=3.5 \mathrm{cm}$

Mass will be proportional to area. So mass of the whole disc is $M=k\pi (14{)}^2$

Mass of cut portion $m_1=k\pi (10.5{)}^2$

Mass of the remaining portion 

$m_2=M-m_1=k\pi \left({14}^2-10.5^2\right)=k\pi (24.5)\times (3.5)$

Now, $m_1{x}_1=m_2{x}_2$

$\Rightarrow x_2=\frac{m_1{x}_1}{m_2}=\frac{k\pi (10.5{)}^2\times 3.5}{k\pi (24.5)\times 3.5}=4.5 \mathrm{cm}$