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A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy ($K_t$) as well as rotational kinetic energy ($K_r$) simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is
Explanation
Total KE of a rolling solid sphere is $\frac{7}{10}mv^2$.
Detailed Solution
$K_t = \frac{1}{2}mv^2$
$K_t + K_r = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 = \frac{1}{2}mv^2 + \frac{1}{2}\left(\frac{2}{5}mr^2\right)\left(\frac{v}{r}\right)^2 = \frac{7}{10}mv^2$
So, $\frac{K_t}{K_t + K_r} = \frac{5}{7}$