(A) Let the origin be at $O$. The area of the large circular plate is $A_1 = \pi(3R)^2 = 9\pi R^2$ and its centre of mass is at $x_1 = 0$.The area of

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(A) Let the origin be at $O$. The area of the large circular plate is $A_1 = \pi(3R)^2 = 9\pi R^2$ and its centre of mass is at $x_1 = 0$.The area of the removed circular hole is $A_2 = \pi R^2$ and its centre of mass is at $x_2 = 2R$.The centre of mass of the remaining system is given by:$\bar{x} = \frac{A_1 x_1 - A_2 x_2}{A_1 - A_2}$Substituting the values:$\bar{x} = \frac{(9\pi R^2)(0) - (\pi R^2)(2R)}{9\pi R^2 - \pi R^2}$$\bar{x} = \frac{-2\pi R^3}{8\pi R^2} = -R/4$The magnitude of the distance from $O$ is $|\bar{x}| = R/4$.

Class 11 Physics System of Particles and Rotational Motion Centre of Mass of Composite Bodies and Cavity Problen of Centre of mass

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In the figure shown,find the distance of the 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 a distance of $2R$ from the centre of the large circular plate.

A
$R/4$
B
$R/5$
C
$R/2$
D
None of these

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System of Particles and Rotational Motion

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Centre of Mass of Composite Bodies and Cavity Problen of Centre of mass

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In the figure shown,find the distance of the 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 a distance of $2R$ from the centre of the large circular plate.

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