A disk of radius 2R and mass 'M' is hinged from its center. If a disk of radius R been removed such that radius of bigger disk behave as a diameter of the disk and it is welded on the opposite side as shown in diagram.Find the ratio of moment of inertia about point ' O ' in Case-I and Case-II :

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Case-I: I 1 ​ = 2 1 ​ M ( 2 R ) 2 = 2 M R 2 Case-II:For small disc about O I = I c m ​ + M d 2 I = 2 1 ​ ⋅ 4 M ​ R 2 + 4 M ​ R 2 = 8 3 ​ M R 2 I 2 ​ = 2 M R 2 I 2 ​ I 1 ​ ​ = 2 M R 2 2 M R 2 ​ = 1

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