First slide

Rolling motion

Question

The ratio of the accelerations for a solid sphere (mass ‘m’ and radius 'R') rolling down an incline plane of angle ' $θ$ ' without slipping and slipping down the incline without rolling is :

Moderate

A

5:7
B

2:3
C

2:5
D

7:5

Solution

For rolling motion without slipping on inclined plane
$a_{1} = \frac{gsin θ}{1 + \frac{K^{2}}{R^{2}}}$
and for slipping motion on inclined plane
$a_{2} = gsin θ$
Required ratio = $\frac{a_{1}}{a_{2}} = \frac{1}{1 + \frac{K^{2}}{R^{2}}} = \frac{1}{1 + \frac{2}{5}} = \frac{5}{7}$

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