A uniform rigid rod of length \( \ell \) and mass \( m \) is hinged at \( O \) in such a way that it can rotate in vertical plane. Initially it is kept vertically as shown in figure. When it is released, it rotates about \( O \) in verticle plane. (consider all surfaces are frictionless).
(A) The magnitude of force given by the hinge to rod at instant when rod becomes horizontal is \( \frac{\sqrt{37}}{4} mg \)
(B) The centre of mass of rod undergoes uniform circular motion
(C) The direction of hinge force is along \( +y \)-axis at instant when centre of mass of rod is at lowest position.
(D) The mechanical energy of rod is not conserved during the motion.