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Question
A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density $\sigma $ at equilibrium position. The extension ${x_0}$ of the spring when it is in equilibrium is:
${{Mg} \over k}$
${{Mg} \over k}\left( {1 - {{LA\sigma } \over M}} \right)$
${{Mg} \over k}\left( {1 - {{LA\sigma } \over {2M}}} \right)$
${{Mg} \over k}\left( {1 + {{LA\sigma } \over M}} \right)$

Solution

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