Question

In the figure shown, the distance of centre of mass of a system of a uniform circular plate of radius $3R$ from O in which a hole of radius $R$ is cut whose centre is at $2R$ distance from centre of large circular plate is :

• A. $R/4$
• B. $R/5$
• C. $R/2$
• D. none of these

Answer 1

The correct option is A $R/4$

Let the mass of whole disc be $M$

So $M=\rho \pi (3R{)}^2=9\rho \pi R^2$

Let the mass of removed disc be $m=\rho \pi R^2\frac{M}{9}$

Center of removed disc from origin is $x_{cm}=3R-R=2R$

So the new CM from from is $x_{new}=\frac{M{X}_{cm}-m{x}_{cm}}{M-m}$

$x_{new}=\frac{M\times 0-\frac{M}{9}\times 2R}{M-M/9}$

$x_{new}=\frac{-R}{4}$, toward the left of O.