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A rod of length L is hinged from one end...

A rod of length `L` is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, When it is in verticle position is

A

`sqrt((2g)/(L))`

B

`sqrt((3g)/(L))`

C

`sqrt((g)/(2L))`

D

`sqrt((g)/(L))`

Text Solution

Verified by Experts

The correct Answer is:
B
Refer to Fig. when the ord goes from position `OA` to `OB`, then loss in `PE` of rod is equal to the gain in `KE` of rotation of rod.
So `mg ((L)/(2)) = (1)/(2)I omega^(2) = (1)/(2) ((mL^(2))/(3))omega^(2)`
or `omega = sqrt((3g)/(L))`
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