A spherical cavity of radius R/2 is cut from a solid sphere of radius R as shown. If the mass of the remaining body is M, what is its moment of inertia about the axis through O shown in the figure?

Question

G1 Physics · Accepted Answer

Treat the removed spherical part as a negative-mass sphere and use the parallel-axis theorem. First express the original-sphere mass and removed-sphere mass in terms of the remaining mass M using the volume ratio. Then compute I of remaining body=I of full sphere-[I of removed sphere,CM+mass of removed sphere d²]. Simplification gives I=57MR²/140. Hence option C.