A rod of length l is hinged at one end. It is | vedclass

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(C) The mass of the rod is concentrated at its center of mass. When the rod is in the horizontal position,its center of mass is at a height $h = \frac

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$\sqrt{\frac{3g}{l}}$

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(C) The mass of the rod is concentrated at its center of mass. When the rod is in the horizontal position,its center of mass is at a height $h = \frac{l}{2}$ from the lowest point. When it reaches the vertical position,the center of mass is at the lowest point.Applying the principle of conservation of mechanical energy:Loss in potential energy $(PE)$ = Gain in rotational kinetic energy $(KE_{rot})$$mg \left(\frac{l}{2}\right) = \frac{1}{2} I \omega^2$Here,$I$ is the moment of inertia of the rod about the hinge at one end,given by $I = \frac{ml^2}{3}$.Substituting the value of $I$:$mg \left(\frac{l}{2}\right) = \frac{1}{2} \left(\frac{ml^2}{3}\right) \omega^2$$mg \frac{l}{2} = \frac{ml^2}{6} \omega^2$$g = \frac{l}{3} \omega^2$$\omega^2 = \frac{3g}{l}$$\omega = \sqrt{\frac{3g}{l}}$

$A$ rod of length $l$ is hinged at one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in the vertical position is

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