Question

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. $\sqrt{\frac{2 g}{L}}$
• B. $\sqrt{\frac{3 g}{L}}$
• C. $\sqrt{\frac{g}{2 L}}$
• D. $\sqrt{\frac{g}{L}}$

Answer 1

Answer: (B)

The rod in potential energy $=$ gain in kinetic energy

$ \Rightarrow m g \frac{L}{2}=\frac{1}{2}\left(\frac{m L^2}{3}\right) \omega^2$
$ \Rightarrow \omega=\sqrt{\frac{3 g}{L}}$