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Question

# A uniform solid sphere of radius R and mass m rolls down an inclined plane. The coefficient of friction between the sphere and the inclined plane is μ then maximum value of θ for pure rolling is

A
tan1(3μ2)
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B
tan1(7μ2)
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C
tan1(5μ3)
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D
tan1(7μ3)
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Solution

## The correct option is B tan−1(7μ2)F.B.D of the uniform solid sphere N=mgcosθ...........(1) mg sin θ−f=ma.........(2) fR=Iα=25mR2×aR [ for uniform rolling, a=αr ] ∴f=25ma.........(3) On putting (3) in (2) mgsinθ=75ma a=57g sin θ..........(4) On putting (4) in (3) f=27mg sin θ Now, for critical case, f≤fsmax=μN ⇒27mg sin θ≤μmg cos θ [ from (1) ] ⇒θ≤tan −1(7μ2)

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