A uniform rod of mass M & length L is hinged about its one end as shown. Initially it is held vertical and then allowed to rotate, the angular velocity of rod when it make an angle of 37° with the vertical is $\sqrt{\frac{ng}{5 L}}$ find n

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answer is 3.

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Detailed Solution

Using work energy theorem,
$\begin{array}{l} Mg \frac{L}{2} (1 - \cos 37) = \frac{1}{2} (\frac{{ML}^{2}}{3}) ω^{2} \\ \Rightarrow \frac{MgL}{2} \times \frac{1}{5} = \frac{{ML}^{2} ω^{2}}{6} \Rightarrow ω = \sqrt{\frac{3 g}{5 L}} \end{array}$

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