Three bodies A, B and C are respectively a disc, a solid sphere and a spherical shell, all of the same mass M and radius R, arranged as shown in the original figure. The moment of inertia of the complete system about axis PQ is (x/15)I, where I = MR²/4 is the moment of inertia of the disc about a diameter. Find x
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Question

Three bodies A, B and C are respectively a disc, a solid sphere and a spherical shell, all of the same mass M and radius R, arranged as shown in the original figure. The moment of inertia of the complete system about axis PQ is (x/15)I, where I = MR²/4 is the moment of inertia of the disc about a diameter. Find x

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G1 Physics · Accepted Answer

Let the common mass and radius be M and R. For disc A, the axis PQ passes through its centre along a diameter, so I A I_A I A ​ = MR²/4. For the solid sphere B, I C M I_CM I C ​ M = (2/5)MR². Its centre is at distance R from PQ, so by the parallel-axis theorem: I B I_B I B ​ = (2/5)MR² + MR² = (7/5)MR². For the spherical shell C, I C M I_CM I C ​ M = (2/3)MR². Its centre is also at distance R from PQ: I C I_C I C ​ = (2/3)MR² + MR² = (5/3)MR². Therefore, I t o t a l I_total I t ​ o t a l = MR²[…