Question

A circular plate of uniform thickness has a diameter $56$cm. A circular portion of diameter $42$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. $5$cm
• B. $7$cm
• C. $9$cm
• D. $11$cm

Answer 1

The correct option is C $9$cm

Let surface mass density $=\sigma$

Mass of $28cm$$diameterplate$=\sigma \pi (0.28)^{ 2 }$

Mass of $21cm$ radius plate$=\sigma \pi (0.21{)}^2$

Take the case where smaller plate has negative mass ad its center is at $C$, in the larger plate.

Now, center of mass is$=\frac{0-=\sigma \pi (0.21{)}^2\times 0.07}{\sigma \pi \left\{\right(0.28{)}^2-\left(0.21{)}^2\right\}}$

$x=\frac{0.07}{0.77}=0.09m$

9cm opposite to the edge where cut from the center $o$.