First slide

Rolling motion

Question

A solid sphere is rolling without sliding on a horizontal surface. Then ratio of its translational kinetic energy to rotational kinetic energy is

Easy

A

3/4
B

2/5
C

5/4
D

5/2

Solution

For rolling without slipping, $V = ω R$
$∴ \frac{K_{T}}{K_{r}} = \frac{\frac{1}{2} m V^{2}}{\frac{1}{2} I ω^{2}} = \frac{\frac{1}{2} m V^{2}}{\frac{1}{2} (\frac{2}{5} m R^{2}) ω^{2}} = \frac{5}{2}$

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