b
       Translational kinetic energy, \({K_t} = \frac{1}{2}m{v^2}\)

Rotational kinetic energy, \({K_r} = \frac{1}{2}I{\omega ^2}\)

\(\begin{array}{ccccc}
\therefore \,{K_t} + {K_r} = \frac{1}{2}m{v^2} + \frac{1}{2}I{\omega ^2}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2}m{v^2} + \frac{1}{2}\left( {\frac{2}{5}m{r^2}} \right){\left( {\frac{v}{r}} \right)^2}\\
\therefore \,{K_t} + {k_r} = \frac{7}{{10}}m{v^2}\,\,\,\,\,\,\left[ {I = \frac{2}{5}m{r^2}\left( {for\,sphere} \right)} \right]\\
So,\,\frac{{{K_t}}}{{{K_t} + {K_r}}} = \frac{5}{7}
\end{array}\)