Answer
See answer.
Work Step by Step
The wheel rotates about its point of contact with the step. Calculate torques with respect to that point. Once the wheel leaves the floor, only two forces exert torques on the wheel: the pulling force F, and the force of gravity.
Calculate the net torque on the wheel, with clockwise torques positive. The minimum pulling force corresponds to a net torque of 0.
$$\Sigma \tau=0=F(R-h)-Mg\sqrt{R^2-(R-h)^2}$$
$$F=\frac{Mg\sqrt{R^2-(R-h)^2}}{R-h}$$
$$F=\frac{Mg\sqrt{2Rh-h^2}}{R-h}$$
