Ratio of Accelerations for Rolling and Slipping Solid Sphere – Rankers Physics

Ratio of Accelerations for Rolling and Slipping Solid Sphere

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $theta$ without slipping and slipping down the incline without rolling is: (2014)

$5 : 7$
$2 : 3$
$2 : 5$
$7 : 5$

Solution:

Acceleration without slipping is $a_1 = \frac{g sin\theta}{1 + I/(mR^2)} = \frac{5}{7}g sin\theta$. Acceleration with pure slipping is $a_2 = g sin\theta$. The ratio $a_1/a_2$ is $5/7$.

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