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From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?

Asked in NEET-I 2016 · Composite and cavity bodies

• (1) 11MR²/32
• (2) 9MR²/32
• (3) 15MR²/32
• (4) 13MR²/32

Step-by-step solution

Why the other options are wrong

• (1) comes from no single slip reaches (11)/(32): the full disc gives (16)/(32)MR² and the hole can take away either 1/(32), its own moment, or 3/(32) with the parallel-axis shift, leaving (15)/(32) or (13)/(32)
• (2) comes from the same test: reaching 9/(32) would need the hole's moment about the disc centre to be 7/(32)MR², more than twice its true value 3/(32)MR²
• (3) comes from subtracting only the hole's moment about its own centre, 1/2(/M4)(/R2)²=(MR²)/(32), and forgetting the parallel-axis shift (/M4)(/R2)²=(2MR²)/(32)

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