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:

Step-by-step solution

The motion of inertia of the system about O , 1 2 M R 2 + 6 × 1 2 M R 2 + 6 × M × 2 R 2 ⇒       I 1 = 7 2 M R 2 + 24 M R 2 The motion of inertia of the system about P , ⇒       I 1 + 7 M D 2 ⇒         7 2 M R 2 + 24 M R 2 + 7 M × 3 R 2 ⇒       181 2 M R 2