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In a system, two connected rigid bars $AC$ and $BC$ are identical length, $L$ with pin supports at $A$ and $B$. The bars are interconnected at $C$ by a frictionless hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, $k$. The system initially assumes a straight line configuration, $ACB$. Assuming both the bars as weightless, the rotation at supports, $A$ and $B$, due to a transverse load, $P$ applied at $C$ is:

  1. $\dfrac{PL}{4k} \\$
  2. $\dfrac{PL}{2k} \\$
  3. $\dfrac{P}{4k} \\$
  4. $\dfrac{Pk}{4L}$
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