A uniform rod AB of weight 100 N rests on a rough peg at C and a force F acts at A as shown in figure. BC = CM, M is the midpoint of AB and tanα
= 4/3. The minimum coefficient of friction at C is

Question

A uniform rod AB of weight 100 N rests on a rough peg at C and a force F acts at A as shown in figure. BC = CM, M is the midpoint of AB and tanα = 4/3. The minimum coefficient of friction at C is

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 9/8.