Question

A solid spherical ball is rolling without slipping down an inclined plane. The fraction of its total energy associated with rotation is

• A. $\frac{2}{5}$
• B. $\frac{2}{7}$
• C. $\frac{3}{5}$
• D. $\frac{3}{7}$

Answer 1

Answer: (B)

$K_R=\frac{1}{2}\left(\frac{2}{5}m{r}^2\right)\frac{v^2}{r^2}$
$K_R=\frac{1}{5}m{v}^2$
$K_{Tr}=\frac{1}{2}m{v}^2$
$K_{\text{Total }}=\frac{1}{5}m{v}^2+\frac{1}{2}m{v}^2$
$=\frac{7}{10}m{v}^2$
$\frac{K_R}{K_{\text{Total }}}=\frac{\frac{1}{5}m{v}^2}{\frac{7}{10}m{v}^2}$
$=\frac{2}{7}$