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in Rotational motion by (25 points)
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.

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