A uniform rod of mass $ M_0 $ and length $ L $ is free to rotate about a pivot at its left end and is released from rest when the rod is $ 30^{\circ} $ below the horizontal, as shown in the figure. With respect to the pivot, the rod has rotational inertia $ I_0 = \dfrac{1}{3} M_0 L^2 $. Which of the following expressions correctly represents the magnitude of the net torque exerted on the rod about the pivot at the moment the rod is released?

Question

A uniform rod of mass $ M_0 $ and length $ L $ is free to rotate about a pivot at its left end and is released from rest when the rod is $ 30^{\circ} $ below the horizontal, as shown in the figure. With respect to the pivot, the rod has rotational inertia $ I_0 = \dfrac{1}{3} M_0 L^2 $. Which of the following expressions correctly represents the magnitude of the net torque exerted on the rod about the pivot at the moment the rod is released?(a) $ M_0 g \left( \dfrac{L}{2} \right) \sin(30^\circ) $
, (b) $ M_0 g \left( \dfrac{L}{2} \right) \sin(60^\circ) $
, (c) $ M_0 g L \sin(30^\circ) $
, (d) $ M_0 g L \sin(60^\circ) $
:

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