A metal ball of mass m is put at the point A of a loop tract and the vertical distance of A from the lower most point of tract is n times the radius R of the circular part. The linear velocity of ball when it rolls to the point B to a height R in the circular tract will be

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G1 Physics · Accepted Answer

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 √[(10/7)g(n-1)R].