Explanation:
Moment of inertia of the upper ring about the axis I
1
=
2
1
mr
2
Moment of inertia of the one of the lower ring about the axis I
2
=
2
1
mr
2
+mr
2
=
2
3
mr
2
Similarly, moment of inertia of the second lower ring about the axis I
3
=
2
3
mr
2
Total moment of inertia of the system about the axis I=I
1
+I
2
+I
3
=
2
7
mr
2
Radius of gyration k=
3m
I
=
6
7
r