1. Given

   • Solid cylinder of mass $M$ and radius $R$
   • A horizontal force $F$ pulls it
   • Rolling without slipping

2. Moment of inertia of a solid cylinder about its axis $I = \frac{1}{2}MR^2$

3. Forces acting on the cylinder

   • Applied force $F$ at the center, toward the right
   • Static friction $f$ at the point of contact

   Since the force is applied at the center, it produces no torque about the center. The torque needed for rotation comes from friction.

4. Translational equation of motion Taking rightward direction as positive: $F - f = Ma$

5. Rotational equation about the center Friction provides torque: $fR = I\alpha$ $fR = \frac{1}{2}MR^2\alpha$ $f = \frac{1}{2}MR\alpha$

6. Rolling without slipping condition $a = \alpha R$ so $\alpha = \frac{a}{R}$

   Substitute into friction expression: $f = \frac{1}{2}MR\left(\frac{a}{R}\right) = \frac{1}{2}Ma$

7. Substitute into translational equation $F - \frac{1}{2}Ma = Ma$ $F = \frac{3}{2}Ma$ $a = \frac{2F}{3M}$

8. Find angular acceleration $\alpha = \frac{a}{R} = \frac{1}{R}\cdot \frac{2F}{3M}$ $\alpha = \frac{2F}{3MR}$

9. Match with options $\boxed{\alpha = \frac{2F}{3MR}}$ This corresponds to Option B.

10. Comparison with stored answer Stored correct answer: B

My derived answer also gives B, so they agree.