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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 ?
|dw:1360249824495:dw| Is this the scenario?
use energy conservative theory:- Potential energy=rotational energy $$\begin{align}mg\frac{l}{2}&=\frac{1}{2}I\omega^2\\ mgl&=\frac{ml^2}{3}\omega^2\\ 3g&=l\omega^2\\ 3g&=l\left(\frac{3v}{l}\right)^2\\ v&=\sqrt{\frac{gl}{3}} \end{align}$$