Question

A circular plate of uniform thickness has a diameter $56\text{cm}$. A circular portion of diameter $42\text{cm}$ is removed from one edge as shown in the figure. The centre of mass of the remaining portion from the centre of plate will be :

• A. $5\text{cm}$
• B. $7\text{cm}$
• C. $9\text{cm}$
• D. $11\text{cm}$

Answer 1

The correct option is C $9\text{cm}$


Let mass of circular plate be $=M$
Mass per unit area $=\frac{M}{\pi (28{)}^2}$
Mass of part removed $=\frac{M}{\pi (28{)}^2}\times \pi (21{)}^2=\frac{9M}{16}$
Mass of remaining part $=\frac{7M}{16}$
Now, $m_1{x}_1=m_2{x}_2$

$\frac{7M}{16}\times x=\frac{9M}{16}\times 7$
$x=9\text{cm}$
The centre of mass of the remaining portion from the centre of plate is $9\text{cm}$.