Question

A thin rod of length $L$ and mass $M$ is held vertically with one end on the floor and is allowed to fall. Find the velocity of the other end when it hits the floor, assuming that the end on the floor does not slip:

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

Answer 1

The correct option is A $\sqrt{\frac{3g}{L}}$

Using Conservation of Energy,

Potential energy=Rotational kinetic energy

$mgh=\left(0.5\right)l{\omega }^2$

$mg\left(\frac{L}{2}\right)=\left(0.5\right)\left(\frac{m{L}^2}{3}\right){\left(\frac{v}{L}\right)}^2$

$mgL=\frac{m{v}^2}{3}$

$\therefore v=\sqrt{\frac{3g}{L}}$