From a circular disc of radius R and mass 9M, a small disc of radius $\frac{\text{R}}{3}$ is removed as shown in Fig. Find the moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the point O.
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Moment of inertia of the complete disc about the given axis $=\frac{1}{2}(9\text{M})\text{R}^2$ Moment of removed disc $=\frac{9\text{M}}{\pi\text{R}^2}\pi\Big(\frac{\text{R}}{3}\Big)^2=\text{M}$ Moment of intertia of this disc about the given axis $=\frac{1}{2}\text{M}\Big(\frac{\text{R}}{3}\Big)^2+\text{M}\Big(\frac{2\text{R}}{3}\Big)^2=\frac{1}{2}\text{MR}^2$ $\therefore$ Moment of inertia of the remaining disc about the given axis $=\frac{9}{2}\text{MR}^2-\frac{1}{2}\text{MR}^2=4\text{MR}^2$
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