A uniform solid sphere rolls down an vertical surface without sliding . If the vertical surface moves with an acceleration a = g/2 , the minimum coefficient of friction between the sphere and the vertical surface so as to prevent relative sliding is ?? Answer is 4/7 .

Dear Student,
mg-μmg2=maa=g-μg2a=Rαα=gR-μg2Rmaximum friction force fmax=μmg2torque=fmaxRμmgR2=2mR2α5μmgR2=2mR25gR-μg2Rμ2=251-μ210μ=8-4μ14μ=8μ=47Regards

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