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Show that the square of the radius of gy...

Show that the square of the radius of gyration of a hollow cylinder is twice that a solid cylinder having the same radius for rotation about the respective cylinder axis.

Text Solution

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For rotation about the cylinder axis moments of inertia of
(1) a thin hollow cylinder, `I_(HC)=Mk_(HC)^2=MR^2`
(2) a solid cylinder, `I_(SC)=Mk_(SC)^2=1/2MR^2`
`therefore k_(HC)^2=R^2=2k_(SC)^2`
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