For rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x 5 . The value of x is _____.

Question

TestHub · Accepted Answer

The rotational kinetic energy is given by

$K_{r o t} = \frac{I ω^{2}}{2} = \frac{1}{3} M R^{2} ω^{2}$ .

The total kinetic energy is given by

$K_{t o t} = \frac{1}{2} m v^{2} + \frac{1}{3} M R^{2} ω^{2} = \frac{m R^{2} ω^{2}}{2} + \frac{1}{3} M R^{2} ω^{2} = \frac{5}{6} M R^{2} ω^{2}$

Thus, the ratio is

$\frac{K_{r o t}}{K_{t o t}} = \frac{\frac{1}{3} M R^{2} ω^{2}}{\frac{5}{6} M R^{2} ω^{2}} = \frac{2}{5}$

Comparing with the given value,

$\frac{x}{5} = \frac{2}{5} \Rightarrow x = 2$

Physics - Rotation Question with Solution | TestHub