Question 1:
moderateThree rings each of mass m and radius r are so placed that they touch each other. The radius of gyration of the system about the axis as shown in the figure is
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,
\[ k= \sqrt{\frac{7}{6}}r \]