Question #42457

This question tests the student's ability to couple translational and rotational dynamics under the constraint of pure rolling.

A common trap is treating the cylinder as a point mass and simply balancing forces at the threshold of sliding ($F = mg \sin\theta - \mu mg \cos\theta$), which yields the incorrect distractor $\frac{25\sqrt{3}}{3} \text{ N}$.

This flawed approach ignores the torque required to maintain the angular acceleration $\alpha = a/R$.

By requiring the static friction to simultaneously satisfy the rotational dynamic equation $f = \frac{1}{2}ma$ and the static threshold $f \le \mu N$, students must realize that the minimum force $F$ is dictated by the friction required to sustain pure rolling, not just translational equilibrium.