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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TestHub · Accepted Answer

The motion of inertia of the system about $O$ ,

$\frac{1}{2} M R^{2} + 6 \times \frac{1}{2} M R^{2} + 6 \times M \times {(2 R)}^{2}$

$\Rightarrow I_{1} = \frac{7}{2} M R^{2} + 24 M R^{2}$

The motion of inertia of the system about $P$ ,

${\Rightarrow I}_{1} + 7 M D^{2}$

$\Rightarrow \frac{7}{2} M R^{2} + 24 M R^{2} + 7 M \times {(3 R)}^{2}$

$\Rightarrow \frac{181}{2} M R^{2}$

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