A uniform rod of length `L` is free to rotate in a vertical plane about a fixed horizontal axis through `B`. The rod begins rotating from rest. The angular velocity `omega` at angle `theta` is given as

Options

A. `sqrt((3g)/(l)) sin(theta//2)`
B. `sqrt((6 g)/(l)) sin (theta//2)`
C. `sqrt((3 g)/(l)) cos (theta//2)`
D. `sqrt((6g)/(l)) cos (theta//2)`

Answer

B

Explanation

(b) Height descended by centre of mass
`h = (l)/(2) - (l)/(2) cos theta`
Loss in `PE` = gain in `KE`
`mgh = (1)/(2) ((ml^2)/(3)) omega^2`
Put the value of `h` and solve to get the answer.
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