A) \[\sqrt{gL}\]
B) \[\sqrt{3gL}\]
C) \[\sqrt{5gL}\]
D) \[3\sqrt{gL}\]
Correct Answer: B
Solution :
Using energy conservation \[\frac{1}{2}I{{\omega }^{2}}=mg\frac{L}{2}\] \[\frac{1}{2}\times m\frac{{{L}^{2}}}{3}{{\omega }^{2}}=mg\frac{L}{2}\] \[{{\omega }^{2}}=\frac{3g}{L};\] \[\omega =\sqrt{\frac{3g}{L}}\] Therefore, \[v=L\omega =L\sqrt{\frac{3g}{L}}=\sqrt{3gL}\]
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