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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

1. 5 : 7
2. 2 : 3
3. 2 : 5
4. 7 : 5

Correct answer: 7 : 5

Solution

For rolling without slipping, the acceleration is derived using both translational and rotational motion, yielding a = (5/7)g sinθ. For slipping without rolling, only translational motion is considered, giving a = g sinθ. The ratio of accelerations is (5/7) : 1, which simplifies to 5 : 7.

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