From a circular disc of radius R and mass $$9M$$, a small disc of radius $$R3is$$ removed as shown in figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

Question

From a circular disc of radius R and mass $$9M$$, a small disc of radius $$R3is$$ removed as shown in figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

Infinity Learn · Accepted Answer

Mass per unit area of $$disc=9M$$$$π$$$$R2Mass$$ of removed portion of $$disc=9M$$$$π$$$$R2$$×π$$R32=MMoment$$ of inertia of removed portion about an axis passing through the centre of disc and perpendicular to the plane of disc, using theorem of parallel axes $$isI1=M2R32+M2R32=12MR2The$$ moment of inertia of complete disc about the given axis is $$I2=92MR2So$$ moment of inertia of the disc with removed portion, about the given axis is $$I=I2$$−$$I1=92MR2$$−$$12MR2=4MR2$$

From a circular disc of radius R and mass 9M, a small disc of radius $\frac{R}{3}$ is removed as shown in figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

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From a circular disc of radius R and mass 9M, a small disc of radius R3is removed as shown in figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

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From a circular disc of radius R and mass 9M, a small disc of radius $\frac{R}{3}$ is removed as shown in figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is