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In the diagram shown below, the rod is u...

In the diagram shown below, the rod is uniform having mass M and length L. When it is making an angle `theta=60^(0)`, the rod is released from the state of rest (and spring in its natural length). The rod comes to state of rest when the angle theta reduces to `30^(@)`. What should be the initial compression in the spring`(when theta = 60^(@))` so that the whole system can remain in the state of rest? (there is no friction between any surfaces)

A

`((sqrt(3)-1))/(2sqrt(3))l`

B

`(3(sqrt(3)-1))/(2)l`

C

`((sqrt(3)-1))/(4sqrt(3))l`

D

`(2(sqrt(3)-1))/(sqrt(3))l`

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