Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis $AB$ as shown in figure is $8/ x$ . The value of $x$ is :

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Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is 8/ x ​ . The value of x is :

TestHub · Accepted Answer

​ I sphere ​ = 3 2 ​ MR 2 = Mk 1 2 ​ I cylinder ​ = 12 1 ​ M ( 4 R 2 ) + 4 1 ​ MR 2 + M ( 2 R ) 2 = 12 67 ​ MR 2 = Mk 2 2 ​ k 2 ​ k 1 ​ ​ = 3 2 ​ ⋅ 67 12 ​ ​ = 67 8 ​ ​ ​

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