A uniform \( \operatorname{rod} A B \) of length \( L \) and mass \( m \) is suspended freely at...

A uniform \( \operatorname{rod} A B \) of length \( L \) and mass \( m \) is suspended freely at \( A \) and hangs vertically at rest when a particle of same mass \( m \) is fired horizontally with speed \( v \) to strike the rod at its mid point. If the particle is brought to rest after the impact. Then the impulsive reaction at \( A \) in horizontal direction is
(a) \( m v / 4 \)
(b) \( m v / 2 \)
(d) \( 2 \mathrm{mv} \)