The ratio of the accelerations 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 (a) 5: 7 (b) 2: 3 (c) 2: 5 (d) 7: 5

Answer: (a). Rolling: a₁ = (gsin θ)/(1 + 2/5) = 5/7gsin θ. Slipping without rolling (frictionless): a₂ = gsin θ. (a₁)/(a₂) = 5/7 So the answer is (a) 5: 7.

The ratio of the accelerations for a solid sphere (mass m and radius… | NEET 2014 (AIPMT)

Q76NEET 2014 · AIPMTEasy

Rolling Motion

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

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Answer: (a)

Rolling: $a_1 = \frac{g\sin\theta}{1 + 2/5} = \frac{5}{7}g\sin\theta$ .
Slipping without rolling (frictionless): $a_2 = g\sin\theta$ .
$\frac{a_1}{a_2} = \frac{5}{7}$
So the answer is (a) 5 : 7.

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