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

Answer

BD

Explanation

`mg (l/2-l/2 sin 30^(@)) =1/2 I omega_(2)^(2)`
`mgl/2=1/2 I omega_(3)^(2)`
`mgl=1/2 Iomega_(4)^(2)`