Question

From a thin circular disc of radius $R$, a circular hole of radius $4R/5$ is cut as shown. The distance of the center of mass of remaining disc, from the center of the original disc is:

• A. $\frac{16R}{45}$
• B. $\frac{R}{3}$
• C. $\frac{R}{4}$
• D. $\frac{16R}{4}$

Answer 1

The correct option is A $\frac{16R}{45}$

Total mass = $M$

mass of $S_1=\frac{M}{R^2\pi }\times \pi {\left(\frac{4R}{5}\right)}^2=\left(\frac{16}{25}\right)M$

com at Bigger disc at centre is

$x\frac{m\left(\frac{a}{25}\right)+m\left(\frac{16}{25}\right)\frac{1}{5}}{m}=0x=\frac{16R}{45}$