question_answer

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

A) \[\sqrt{\frac{2g}{L}}\]                   

B) \[\sqrt{\frac{3g}{L}}\]

C) \[\sqrt{\frac{g}{2L}}\]                   

D) \[\sqrt{\frac{g}{L}}\]

Correct Answer: B

Solution :

                The rod in potential energy = gain in kinetic energy \[mg\frac{L}{2}=\frac{1}{2}\left( \frac{m{{L}^{2}}}{3} \right){{\omega }^{2}}\] \[\omega =\sqrt{\frac{3g}{L}}\]