A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt ) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr ) for the sphere is :
Answer & explanation
Correct answer: option 2
Kt = \(\frac{1}{2}m v^2\)
Kt + Kr = \(\frac{1}{2}m v^2\) + \(\frac{1}{2}I \omega^2\)
Kt + Kr = \(\frac{1}{2}m v^2\) + \(\frac{1}{2} (\frac{2}{5}m r^2) (\frac{v}{r})^2 \)
\(\frac{K_t}{K_t + K_r}\) = \(\frac{5}{7}\)