A uniform disc has mass M and radius R. A circular disc of radius R/3 is removed from it as shown in the original figure. The moment of inertia of the remaining part about the original central axis AB perpendicular to the plane is (4/x)MR². Find x.

Question

G1 Physics · Accepted Answer

Moment of inertia of the complete disc about its central perpendicular axis is I f u l l I_full I f ​ u l l = ½MR². The removed disc has radius R/3. Since the original disc is uniform, removed mass is proportional to area: m = M(R/3)²/R² = M/9. From the figure, the small removed disc is internally tangent to the large disc, so its centre is at distance d = R-R/3 = 2R/3 from the original centre O. Moment of inertia of the removed disc about its own centre: I c m I_cm I c ​ m = ½m(R/3)² = ½(M/9)(…