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.
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