Question

If a sphere is rolling, the ratio of its rotational energy to the total kinetic energy is given by

• A. 7:10
• B. 2:05
• C. 10:07
• D. 2:07

Answer 1

The Correct Option is D

For a solid sphere rolling down Translation $KE =\frac{1}{2} M v^{2}$
Rotational $K E=\frac{1}{2} I \omega^{2}$
$=\frac{1}{2}\left[\frac{2}{5} M R^{2}\right]\left[\frac{v}{R}\right]^{2}$
$\begin{bmatrix}\text { As for a sphere } \\ I=\frac{2}{5} M R^{2}\end{bmatrix}$
$\therefore$ Total kinetic energy of rolling is
$\frac{1}{2} M v^{2}+\frac{1}{5} M v^{2}=\frac{7}{10} M v^{2}$
$\therefore$ Ratio of rotational kinetic energy to total
kinetic energy $=\frac{\frac{1}{5} M v^{2}}{\frac{7}{10} M v^{2}}=\frac{2}{7}$