# A rod so long!

Consider a thin rod having length same as earth's radius $$R=6371 Km$$ and uniformly distributed mass $$m = 20 Kg$$. Its lower end is just above earth's surface as shown in the figure. The rod is hinged about $$O$$

Find the time period of small angular oscillations of the rod in seconds.

Details and assumptions

• Value of $$g$$ near surface of earth = $$9.8 m/s^2$$.

• You may neglect friction and air resistance.

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