\(K _{\text {Rother }}= K _{\text {Trenstation }}+ K _{\text {rotaton }}\)

\(=\frac{1}{2} m v^2+\frac{1}{2} l \omega^2\)

\(=\frac{1}{2} m R^2 \omega^2+\frac{1}{2}\left|\omega^2=\frac{1}{2}\right| \omega^2\left(1+\frac{m R^2}{1}\right)\)

\(\Rightarrow\) ratio \(=\frac{K_{\text {waton }}}{K_{\text {total }}}=\frac{\frac{1}{2} I ^2}{\frac{1}{2} I_{\omega^2}\left(1+\frac{m R^2}{1}\right)}\)

\(=\frac{1}{1+\frac{m R^2}{1}}\)

For disc,

\(\text { Ratio }=\frac{1}{1+\frac{m R^2}{\left(\frac{m R^2}{2}\right)}}=\frac{1}{3}\)

Solid sphere

\(\text { Ratio }=\frac{1}{1+\frac{m R^2}{\frac{2}{5} m R^2}}=\frac{2}{7}\)

Ring

\(\text { Ratio }=\frac{1}{1+\frac{m R^2}{m R^2}}=\frac{1}{2}\)

Hollow sphere ratio \(=\frac{1}{1+\frac{m R^2}{\frac{2}{3} m R^2}}=\frac{2}{5}\)

Hence \(ring\) correct option.