Find ratio of radius of gyration of a disk and ring of same radii at their tangential axis in plane.

Step-by-step solution

For disk, moment of inertia about the diameter, I _ d = mr ^2 4 and moment of inertia about the tangential axis aligned & I _ disc = I _ d + mr ^2 & I _ disc = mr ^2 4 + mr ^2 & I _ disc = 5 mr ^2 4 aligned Let the radius of gyration of disc is k _ disc . aligned I _ disc & = mk _ disc ^2 5 mr ^2 4 & = mk _ disc ^2 k _ disc ^2 & = 5 4 r aligned For ring, moment of inertia about the diameter I _ a ^ = mr ^2 / 2 and moment of inertia about the tangential axis I _ ring = I _ a ^ + mr ^2= mr ^2 2 + mr ^2= 3 2 mr ^2 Let