Question

A thin uniform rod of mass $M$ and length $L$ is hinged vertically above frictionless pivot point $O$, as shown in figure and then allowed to fall to the ground. With what speed does the free end of the rod strike the ground?

• A. $\sqrt{\frac{1}{3}gL}$
• B. $\sqrt{gL}$
• C. $\sqrt{3gL}$
• D. $\sqrt{2gL}$

Answer 1

The correct option is C $\sqrt{3gL}$

By conservation of energy
$Mg\left(\frac{L}{2}\right)+0=0+\frac{1}{2}I{\omega }^2$

$=\frac{1}{2}\frac{M{L}^2}{3}{\omega }^2$

$\omega =\sqrt{\frac{3g}{L}}$

Speed of end point of the rod=$\omega L=\sqrt{3gL}$