A thin uniform rod of mass and length is pivoted at a height as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is [2026]

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Solution

Q.
A thin uniform rod $(X)$ of mass $M$ and length $L$ is pivoted at a height $(\frac{L}{3})$ as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is __________.

(g = gravitational acceleration) [2026]

1 $\sqrt{\frac{3}{2} \frac{g}{L}}$

2 $\frac{3}{\sqrt{2}} \sqrt{\frac{g}{L}}$

3 $\frac{1}{\sqrt{2}} \sqrt{\frac{g}{L}}$

4 $\sqrt{\frac{3 g}{L}}$

Ans.
(4)

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