A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre 'O' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is:

A

$$Mg\sqrt{1 - \left(\frac{R-a}{R}\right)^2}$$

B

$$Mg\sqrt{\left(\frac{R}{R-a}\right)^2 - 1}$$

C

$$Mg\frac{a}{R}$$

D

$$Mg\sqrt{1 - \frac{a^2}{R^2}}$$