A) \[{{f}_{0}}\]
B) \[\sqrt{2}{{f}_{0}}\]
C) \[2{{f}_{0}}\]
D) \[2\sqrt{2}{{f}_{0}}\]
Correct Answer: B
Solution :
\[{{f}_{0}}=\frac{1}{2\pi }\sqrt{\frac{mg\ell }{\ell }}\] where, \[\ell \] is the distance between point of suspension and centre of mass of the body. Thus, for the stick of length L and mass m, \[{{f}_{0}}=\frac{1}{2\pi }\sqrt{\frac{mg\frac{L}{4}}{\frac{m}{2}\frac{{{(L/2)}^{2}}}{12}}}=\frac{1}{2\pi }\sqrt{\frac{12g}{L}}=\sqrt{2\,}{{f}_{0}}\]
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