A rod so long!

Classical Mechanics Level 5

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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