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. (2g/L)
• B. (3g/L)
• C. (g/2L)
• D. (g/L)

Answer 1

The correct option is B (3g/L)

$\Delta u=mg\frac{l}{2}\Delta u=\Delta KEKE=\frac{1}{2}I{\omega }^2=\frac{1}{2}\left(\frac{1}{3}m{l}^2\right){\omega }^2\Rightarrow \frac{1}{6}m{l}^2{\omega }^2=\frac{mgl}{2}\Rightarrow \omega =\sqrt{\frac{3g}{l}}$