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Question 30362
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Rigid Body Dynamics: JEE — Sphere Rolling Up MCQ

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JEE — Sphere Rolling UpHardQuestion 30362

Question

A solid sphere rolls without slipping up a rough incline (θ = 30°). The magnitude of the acceleration of its centre of mass is (g = 10 m/s²):
  1. A
    5 m/s²
  2. B
    3.57 m/s²
    Correct
  3. C
    7 m/s²
  4. D
    6 m/s²

Correct answer

3.57 m/s²

Explanation

For rolling without slipping, a=gsin⁡θ/[1+I/(mR2)]a=g\sinθ/[1+I/(mR^2)]. For a solid sphere I/(mR2)=2/5I/(mR^2)=2/5, so a=10(1/2)/(7/5)=<strong>25/7≈3.57 m/s2</strong>a=10(1/2)/(7/5)=<strong>25/7≈3.57\text{ m/s}^2</strong> down the incline.

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