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A thin rod free to rotate about a horizo...

A thin rod free to rotate about a horizontal axis through one end O is initially is unstable equilibrium position 1 and falls due to gravity on being displaced infinetsimally. In positions 2,3 and 4 it makes `60^@, 90^@` and `180^@` with the upward vertical. Let `omega_2, omega_3` and `omega_4` be angular velocities of the rod in these positions then

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