d
\({{{E_{Sphere}}}}{{{E_{Cylinder}}}} = \frac{{\frac{1}{2}{I_s}\omega _s^2}}{{\frac{1}{2}{I_c}\omega _c^2}} = \frac{{{I_s}\omega _s^2}}{{{I_c}\omega _c^2}}\)
Here,\({I_s} = \frac{2}{5}m{R^2},{I_c} = \frac{1}{2}m{R^2}\)
\({\omega _c} = 2{\omega _s}\)
\({{{E_{Sphere}}}}{{{E_{Cylinder}}}} = \frac{{\frac{2}{5}m{R^2} \times \omega _s^2}}{{\frac{1}{2}m{R^2} \times {{\left( {2{\omega _s}} \right)}^2}}} = \frac{4}{5} \times \frac{1}{4} = \frac{1}{5}\)