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Question

A solid sphere of mass 7 kg rolls without slipping on an inclined plane of inclination 60∘. What should be the minimum coefficient of static friction to support pure rolling?

A
3
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B
237
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C
27
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D
32
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Solution

The correct option is B 2√37 Given, the sphere is rolling without sliding. Hence, a=αR ...(i) From, ∑τcom=Icomα −f×R=−25mR2×α or f=25mRα=25ma ...(ii) [using (i)] Applying Newton's 2nd law, ∑→Fext=m→acom mgsinθ−f=ma ...(iii) Putting (1) & (ii) in (iii) mgsinθ−25ma=ma a=5gsinθ7 & f=2mgsinθ7 We know, (fs)max=μN=μmgcosθ and, f≤[(fs)max] ⇒2mgsinθ7≤μmgcosθ ⇒μ≥27tanθ ∴μmin=27tan60∘=2√37

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