When a body is under pure rolling, the fraction of its total kinetic energy which is purely rotational is 2/5. Identify the body.

Question

When a body is under pure rolling, the fraction of its total kinetic energy which is purely rotational is $\frac{2}{5}$ . Identify the body.

Smart Achievers · Accepted Answer

(1)

$\frac{Rotational K.E.}{Total K.E.} = \frac{2}{5}$

$\Rightarrow \frac{\frac{1}{2} I ω^{2}}{\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}} = \frac{2}{5}$

$\Rightarrow \frac{\frac{1}{2} m K^{2} ω^{2}}{\frac{1}{2} m R^{2} ω^{2} + \frac{1}{2} m K^{2} ω^{2}} = \frac{2}{5}$

$\Rightarrow \frac{K^{2}}{K^{2} + R^{2}} = \frac{2}{5}$

$\Rightarrow K^{2} = \frac{2}{3} R^{2}$ $or$ $K = \sqrt{\frac{2}{3}} R$

$So it will be hollow sphere.$

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