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Q.
A solid spherical ball is rolling without slipping down an inclined plane. The fraction of its total energy associated with rotation is
System of Particles and Rotational Motion
Solution:
$K_{R}=\frac{1}{2}\left(\frac{2}{5} m r^{2}\right) \frac{v^{2}}{r^{2}}$
$K_{R}=\frac{1}{5} m v^{2}$
$K_{T r}=\frac{1}{2} m v^{2}$
$K_{\text {Total }}=\frac{1}{5} m v^{2}+\frac{1}{2} m v^{2}$
$=\frac{7}{10} m v^{2}$
$\frac{K_{R}}{K_{\text {Total }}}=\frac{\frac{1}{5} m v^{2}}{\frac{7}{10} m v^{2}}$
$=\frac{2}{7}$