A solid uniform disk of mass m rolls without slipping down a fixed inclined plane with an acceleration a. The frictional force on the disk due to surface of the plane is:
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A solid uniform disk of mass m rolls without slipping down a fixed inclined plane with an acceleration a. The frictional force on the disk due to surface of the plane is:

G1 Physics · Accepted Answer

For a solid disc rolling down an incline, I=½mR². Equations mg sinθ-f=ma and fR=I(a/R) give f=ma/2. Hence D. Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives ma/2..