velocity \((v)=2 m / s .\) Radius \((r)=0.5 \mathrm{m}\)

NOW

Total \(\mathrm{KE}(\mathrm{E})=\mathrm{E}_{\text {transalational }}+\mathrm{E}_{\text {rotational }}\)

\(\Rightarrow E=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2}\)

\(\Rightarrow \mathrm{E}=\frac{1}{2} m v^{2}+\frac{1}{2} m k^{2}\left(\frac{v}{r}\right)^{2},\) where \(\mathrm{k}=\) radius of gyration

\(\Rightarrow 32.8=\frac{1}{2} \times 10 \times 2^{2}+\frac{1}{2} \times 10 \times k^{2}\left(\frac{2}{0.5}\right)^{2}\)

\(\Rightarrow 32.8=20+80 \times k^{2}\)

\(\Rightarrow k^{2}=\frac{12.8}{80}=0.16\)

\(\Rightarrow k=0.4 m\)