Question

Find ratio of rotational and translation kinetic energy of a rolling sphere.

• A. $\frac{2}{5}$
• B. $\frac{2}{3}$
• C. $\frac{1}{6}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{2}{5}$

For rolling sphere,

Translation K.E$=T_{K.E}=\frac{1}{2}m{v}^2$

Potential K.E$=R_{K.E}=\frac{1}{2}I{\omega }^2$

where $I=\frac{2}{5}m{R}^2$ and $V=R\omega$

$\therefore T_{K.E}=\frac{1}{2}m{R}^2{\omega }^2$

any $R_{K.E}=\frac{1}{2}\times \frac{2}{5}m{R}^2{\omega }^2=\frac{1}{5}m{R}^2{\omega }^2$

$\therefore \frac{R_{K.E}}{T_{K.E}}=\frac{\frac{1}{5}m{R}^2{\omega }^2}{\frac{1}{2}m{R}^2{\omega }^2}=\frac{2}{5}$.