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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:
A
5 : 7
B
2 : 3
C
2 : 5
D
7 : 5
Detailed Solution
Rolling without slipping: $a_1 = \frac{g\sin\theta}{1 + \frac{K^2}{R^2}}$
Slipping without rolling: $a_2 = g\sin\theta$
$\frac{a_1}{a_2} = \frac{1}{1 + \frac{K^2}{R^2}} = \frac{1}{1 + \frac{2}{5}} = \frac{5}{7}$
Slipping without rolling: $a_2 = g\sin\theta$
$\frac{a_1}{a_2} = \frac{1}{1 + \frac{K^2}{R^2}} = \frac{1}{1 + \frac{2}{5}} = \frac{5}{7}$