A thin uniform rod of mass \( m \) and length \( l \) is hanging freely from its topmost point a...

A thin uniform rod of mass \( m \) and length \( l \) is hanging freely from its topmost point and is free to rotate about its upper end. When it is at rest, it receives an impulse \( J \) at its lowest point normal to its length. Immediately after :
(A) The angular momentum of the \( \operatorname{rod} \) is \( \mathrm{J} l \)
(B) Angular velocity of the \( \operatorname{rod} \) is \( 3 \mathrm{~J} / \mathrm{m} l \)
(C) The K.E. of the rod is. \( 3 \mathrm{~J}^{2} / 2 \mathrm{~m} \)
(D) The linear velocity of the midpoint of the rod is \( 3 \mathrm{~J} / 2 \mathrm{~m} \).