Two identical rigid slender bars of length $2$ L and mass $m$ are acted upon by a transverse force F at one of the ends as shown in the figure. In the first case, the bar is pinned at the other end. In the second case, the bar is pinned at its mid-point. What should be the magnitude of the force F such that the resulting angular accelerations of the two bars are equal?
- $m g$
- $\frac{m g}{2}$
- $\frac{m g}{4}$
- $\frac{m g}{6}$
