A solid sphere of mass 7kg 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
2√37
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C
27
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D
√32
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Solution
The correct option is B2√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