Seven identical circular planar disks, each of mass M and radius R… | JEE Main 2018

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Moment of Inertia & Radius of Gyration

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:

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Answer: (a)

About O: centre disc $\frac{MR^2}{2}$ ; each outer disc $\frac{MR^2}{2} + M(2R)^2 = \frac{9}{2}MR^2$ .
$I_O = \frac{1}{2}MR^2 + 6 \times \frac{9}{2}MR^2 = \frac{55}{2}MR^2$
P is $3R$ from O, total mass $7M$ : $I_P = \frac{55}{2}MR^2 + 7M(3R)^2$
$I_P = \frac{55 + 126}{2}MR^2 = \frac{181}{2}MR^2$ , so the answer is (a).

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