Parallel and Perpendicular Axis Theorem: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Parallel and Perpendicular Axis Theorem. Understanding the underlying formula is key to arriving at the correct answer below:

Moment of Inertia of ring about it's diameter is mR²/2.  ( Using Perpendicular axis theorem)

Moment of Inertia about tangential axis in plane of ring will be mR²/2 + mR²= 3/2 mR²

Total moment of inertia about the axis shown in figure

=  (3/2 mR² )× 2 + 1/2 mR²= 7/2 mR²

Radius of Gyration is k then 3m×k²= 7/2 mR²

so,

\[ k= \sqrt{\frac{7}{6}}r \]