First slide

Rolling motion

Question

A round object is rolling without sliding on a horizontal surface. If ratio of its translational energy to total energy is 2 : 3, then the object is a

Moderate

A

Thin spherical shell
B

Thin ring
C

Solid sphere
D

Solid disc

Solution

$\frac{\frac{1}{2} m V^{2}}{\frac{1}{2} m V^{2} + \frac{1}{2} I_{C} {(\frac{V}{R})}^{2}} = \frac{2}{3} \Rightarrow \frac{1}{1 + \frac{I_{C}}{m R^{2}}} = \frac{2}{3} \Rightarrow I_{C} = \frac{1}{2} m R^{2}$

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