First slide

Rolling motion

Question

The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline 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

Acceleration of sphere when it is slipping down the incline, $a_{slipping} = g \sin θ$
Acceleration of sphere when it is rolling down
$a_{rolling} = \frac{g sinθ}{1 + \frac{K^{2}}{r^{2}}} = \frac{5}{7} g \sin θ$
Hence required ratio $\frac{a_{rolling}}{a_{slipping}} = \frac{5}{7}$

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