c
For ring \(I=m R_1^2=m K_1^2\)

\(\therefore\) Radius of gyration \(K_1=R_1\)

For solid sphere

\(I^{\prime}=\frac{2}{5} m^{\prime} R_2^2=m^{\prime} K_2^2\)

\(\therefore \text { Its radius of gyration }=K_2=\sqrt{\frac{2}{5}} R_2\)

\(\because K_1=K_2\)

\(\therefore R_1=\sqrt{\frac{2}{5}} R_2\)

\(\therefore \frac{R_1}{R_2}=\sqrt{\frac{2}{5}}\)

\(\therefore x=5\)