A ring and a solid sphere rotating about axes through their centres have the same radius of gyration. The ring axis is perpendicular to its plane. The ratio of radius of ring to radius of sphere is √(2/x). Find x.
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 2 Evening Shift

Question

A ring and a solid sphere rotating about axes through their centres have the same radius of gyration. The ring axis is perpendicular to its plane. The ratio of radius of ring to radius of sphere is √(2/x). Find x.

Physics · Circular Motion

JEE Mains 6 April 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

Radius of gyration k is defined by I = Mk² For a ring about its central perpendicular axis: I = MR(ring)² So, k = R(ring) For a solid sphere about a diameter: I = (2/5)MR(sphere)² So, k = √(2/5) R(sphere) Equal radii of gyration give R(ring)/R(sphere) = √(2/5) The question writes this ratio as √(2/x). Therefore x = 5. Final value: 5