First slide

Rolling motion

Question

A uniform solid sphere is executing pure rolling without sliding on a rough horizontal surface. The ratio of its rotational kinetic energy to the total kinetic energy due to rolling is

Easy

A

$\frac{2}{3}$
B

$\frac{2}{5}$
C

$\frac{2}{7}$
D

$\frac{1}{3}$

Solution

kinetic energy due to rotation $\frac{1}{2} I_{c o m} ω^{2} = \frac{1}{2} \frac{2}{5} m r^{2} ω^{2}$
Kinetic energy due to rolling $\frac{1}{2} m v^{2} + \frac{1}{2} I_{c o m} ω^{2}$

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