A uniform rod of mass \( m \) and length \( l \) is fixed from point \( A \), which is at a dist...

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A uniform rod of mass \( m \) and length \( l \) is fixed from point \( A \), which is at a distance \( l / 4 \) from one end as shown in the figure. The rod is free to rotate in a vertical plane. The rod is released from the horizontal position.

What is the reaction at the hinge, when kinetic energy of the rod is maximum?
(1) \( \frac{4}{7} m g \)
(2) \( \frac{5}{7} m g \)
(3) \( \frac{13}{7} m g \)
(4) \( \frac{11}{7} m g \)
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