The wheel will roll up if the torque due to the horizontal force (tau_F) exceeds the torque due to the force of gravity (tau_g) .
tau_g=Mgsin(alpha)=Mg[sqrt(R^2-(R-h)^2)/R]
tau_F=Fcos(alpha)=F(R-h)/R
tau_Fgttau_g
F(R-h)/RgtMg[sqrt(R^2-(R-h)^2)/R]
FgtMg*sqrt(R^2-(R-h)^2)/(R-h)
This is the solution. Notice if h->R Then F ->oo . If h->0 , F->0 . This is intuitively reasonable.
http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html
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