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A squirrel of mass $m$ climbs slowly on a thin straight vertical rod of length $L$. Mass of the rod is negligible as compared to that of the squirrel and size of the squirrel is negligible as compared to the length $l$ that it climbs on the rod. Due to weight of the squirrel, the rod bends at its lower end through an angle $\theta$ and due the elasticity of the material of the rod a restoring torque $C\theta$ is developed. If $C=2mgL$, find the maximum length the squirrel can climb on the rod. enter image description here

I tried to solve this problem by balancing the torque of the weight of the squirrel and the restoring torqe $$mgl\sin\theta=2mgL\theta$$ but this equation gives me $l\approx2L$. But as the length of the rod is $L$, so it means that squirrel would have climbed the whole rod.
But when the squirrel just started climbing the rod, restoring torque must have been $2mgL\theta$ and torque of squirrel's weight is $mgl\theta$ ($\sin\theta\approx\theta $ for small $\theta$). Which is clearly less than the restoring torque. So according to me the squirrel must not be able to climb the rod at all, which is not the case. So aren't the two things contradicting each other? What is the reason for this contradiction?

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    $\begingroup$ "Due to weight of the squirrel, the rod bends at its LOWER END through an angle θ and due the ELASTICITY of the material of the rod a restoring torque Cθ is developed." So what I think is that only the lower part is bending by angle θ and maybe after the squirrel is halfway across the rod the angle no longer remains θ. $\endgroup$
    – Stack3002
    Aug 25, 2021 at 12:48
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    $\begingroup$ A second approach is that l = 2L so meaning that in theory the squirrel can climb twice the length and practically, it can travel the whole length. What I think is that perhaps the question lacks information. So please confirm if there is more information regarding the question. $\endgroup$
    – Stack3002
    Aug 25, 2021 at 12:54
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    $\begingroup$ If any of my approaches is correct inform me and I will write a detailed answer after research and if I am wrong please do so as to correct me. $\endgroup$
    – Stack3002
    Aug 25, 2021 at 12:56
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    $\begingroup$ I don't think the question should be closed. @nimit jain was confused whether he had missed any concepts in the question. At the same time he showed us what he had done by writing appropriate equations and nowhere did he write the answer and expect others to check-his-work. $\endgroup$
    – Stack3002
    Aug 25, 2021 at 13:45
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    $\begingroup$ ... restoring torque must have been 2mgLθ and torque of squirrel's weight is mglθ (sinθ≈θ for small θ). Which is clearly less than the restoring torque. So according to me the squirrel must not be able to climb the rod at all, which is not the case. I would re-think this last sentence. $\endgroup$
    – Jim Clark
    Aug 25, 2021 at 15:43

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