For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is ?. The value of is ________. [2023]

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Solution

Q.
For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$ . The value of $x$ is ________. [2023]

Ans.
(2)

$\frac{K_{rot}}{K_{total}} = \frac{\frac{1}{2} (\frac{2}{3} m R^{2}) {(\frac{v}{R})}^{2}}{\frac{1}{2} m v^{2} + \frac{1}{2} (\frac{2}{3} m R^{2}) {(\frac{v}{R})}^{2}}$

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

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