A uniform cylinder of mass M and radius R

For step up, $F \times R \geq M g \times x$

$x=\sqrt{R^{2}-(R-a)^{2}}$ from figure

$F_{\min }=\frac{M g}{R} \times \sqrt{R^{2}-(R-a)^{2}}=M g \sqrt{1-\left(\frac{R-a}{R}\right)^{2}}$