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:

Question

G1 Physics · Accepted Answer

Image For the hollow sphere: I(sphere) = (2/3)MR² = Mk₁² So: k₁² = 2R²/3 For the solid cylinder shown: Radius = 2R Length = 4R Moment of inertia about the transverse central axis: I(cylinder) = (1/12)M(4R)² + (1/4)M(2R)² + M(2R)² = (67/12)MR² = Mk₂² Therefore: k₁/k₂ = √[(2/3)/(67/12)] = √(8/67) Hence: x = 67