Question

A pencil of lenght l placed vertically on a smooth falls down. The linear velocity of a point on the pencil at a distance l/3 from bottom end of pencil when it is about to land on the table is ?

Answer 1

Is this the scenario?

Answer 2

Yes

Answer 3

use energy conservative theory:-

Potential energy=rotational energy

$$\begin{align}mg\frac{l}{2}&=\frac{1}{2}I\omega^2\\
mgl&=\frac{ml^2}{3}\omega^2\\
3g&=l\omega^2\\
3g&=l\left(\frac{3v}{l}\right)^2\\
v&=\sqrt{\frac{gl}{3}}
\end{align}$$

Answer 4

correct!