The ratio of the 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 (cylinder radius R, length 2R, with AB at distance 2R from its centre), is √8/x. The value of x is .

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Accepted Answer

67. Hollow sphere about a diameter: k₁²=2/3 R². Cylinder about AB: I₂=(M(2R)²)/(12)+(MR²)/4+M(2R)²=(67)/(12)MR², so k₂²=(67)/(12)R². (k₁²)/(k₂²)=(2/3)/(67/12)=8/(67), so x=67.

The ratio of the 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 (cylinder radius R, length 2R, with AB at distance 2R from its centre), is √8/x. The value of x is ______.

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