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Question 30352
JEE Physics · Hard

Rigid Body Dynamics: Pure Rolling — Incline Condition MCQ

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Pure Rolling — Incline ConditionHardQuestion 30352

Question

For a sphere (k = 2/5) to roll without slipping down an incline of angle θ, the minimum coefficient of static friction required is:
  1. A
    (2/7)tanθ
    Correct
  2. B
    (5/7)tanθ
  3. C
    (2/5)tanθ
  4. D
    tanθ/2

Correct answer

(2/7)tanθ

Explanation

For rolling without slipping: friction f = Ma × (k/(1+k)) and N = Mg cosθ. μ_min = f/N = [(k/(1+k)) × g sinθ] / (g cosθ) = (k/(1+k))tanθ = (2/5)/(1+2/5) × tanθ = (2/5)/(7/5) × tanθ = (2/7)tanθ.

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