Question

The ratio of the radii of gyration of a hollow cone and a hollow cylinder of the same mass and radius about a tangential axis parallel to their central axis is:

• A. \(\sqrt{3} : \sqrt{2}\)
• B. \(\sqrt{3} : 2\)
• C. \(1 : \sqrt{2}\)
• D. \(\sqrt{5} : \sqrt{6}\)

Hint:

For a thin hollow cylinder about its own axis: \[ I = MR^2 \] For a hollow cone about its own axis: \[ I = \frac{1}{2}MR^2 \] Always apply the Parallel Axis Theorem carefully when shifting to a tangential axis.

Answer 1

The Correct Option is B