Question

# A sphere of mall 5 kg rolls without slipping on an inclined plane of inclination 30∘. Choose the correct statement(s). Force of friction acting on sphere is 5g7.Linear acceleration of sphere down the plane is 5g14.For pure rolling, μ>0.165.None of these

Solution

## The correct options are A Force of friction acting on sphere is 5g7. B Linear acceleration of sphere down the plane is 5g14. C For pure rolling, μ>0.165. N= Normal force f= friction force mg= weight of sphere Let the linear acceleration of the sphere down the plane be a. So, equation of linear motion for the centre of mass  mgsinθ−f=ma.....(1) ∵ Sphere rolls without slipping  So α=ar where α=Angular acceleration, a=Linear acceleration For Rotational motion,  τ0=Iα where τ0= Torque about centre of mass ⇒fr=25mr2(ar) ⇒f=25ma......(2) From eq (1) & (2) mgsinθ=75ma ⇒a=57gsinθ=57×g×sin30∘=514g ⇒a=5g14 and f=27mgsinθ=27×5×g×12=5g7 f=5g7 For pure rolling, fmax≥fkinetic ⇒μmgcosθ≥27mgsinθ ⇒μ≥27tan θ=0.165 i.e μ>0.165 Options A, B & C are correct.

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