$(a)\;\sqrt{\large\frac{3g}{2L}}\qquad(b)\;\sqrt{\large\frac{g}{L}}\qquad(c)\;\sqrt{\large\frac{4g}{5L}}\qquad(d)\;\sqrt{\large\frac{3g}{L}}$

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Answer : (a) $\;\sqrt{\large\frac{3g}{2L}}$

Explanation :

As it is displaced by small angle $\;\theta$

Taking torque about O

$mgsin \theta\times \large\frac{L}{2}=I \alpha$

$mgsin \theta\times \large\frac{L}{2}=\large\frac{mL^3}{3} \alpha \quad $ for small values of $\;\theta \; sin \theta \approx \theta$

$mg \theta \times \large\frac{L}{2}=\large\frac{L}{3}\times \alpha$

$\alpha=\large\frac{3g}{2L}\;\theta$

$w=\sqrt{\large\frac{3g}{2L}}$

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