Question

From a disc of radius $R$ a smaller disc of radius $R/4$ is removed as shown in figure. Distance of centre of mass of the remaining part from centre of the bigger disc is:-

• A. $\frac{R}{10}$
• B. $\frac{R}{20}$
• C. $\frac{R}{16}$
• D. $\frac{R}{5}$

Answer 1

Answer: (B)

$m_{1}=m,m_{2}=\frac{m}{\pi R^{2}}\times \pi \left(\frac{R}{4}\right)^{2}=\frac{M}{16}$
$x_{cm}=\frac{m_{1} x_{1} - m_{2} x_{2}}{ m_{1} - m_{2}}=\frac{m \left(0\right) - \frac{m}{16} \left(\frac{3 R}{4}\right)}{m - \frac{m}{16}}$