Question

A uniform rod of length 50 cm is released in the vertical plane from the position shown in figure. The rod is hinged smoothly at O. The angular speed of rod when it becomes horizontal is :

• A. 30 rad/s
• B. $\sqrt{30}rad/s$
• C. 40 rad/s
• D. $\sqrt{32}$ rad/s

Answer 1

The correct option is B $\sqrt{30}rad/s$

$\frac{1}{2}l{\omega }^2=Mg\frac{L}{4}$
$\Rightarrow \frac{1}{2}\frac{M{L}^2}{3}{\omega }^2=Mg\frac{L}{4}$
$\Rightarrow {\omega }^2=\frac{3}{2}\frac{g}{L}=\frac{3\times 10}{2\times \frac{1}{2}}=30$
$\omega =\sqrt{30}$ rad/s