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Q.
A circular hole of radius $\left(\frac{a}{2}\right)$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :
JEE MainJEE Main 2021System of Particles and Rotational Motion
Solution:
Let $\sigma$ be the uniform mass density of disc then
$x _{ COM }=\frac{\left(\sigma \pi a ^{2}\right) a -\sigma \pi\left(\frac{ a ^{2}}{4}\right) \times \frac{3 a }{2}}{\sigma \pi a ^{2}-\frac{\sigma \pi a ^{2}}{4}}$
$=\frac{a-\frac{3 a}{8}}{1-\frac{1}{4}}=\frac{5 a}{6}$
