A uniform cylinder of length \( L \) and mass \( M \) having cross sectional area \( A \) is sus...

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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 massless 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
[JEE (Mains) 2013]
(a) \( \frac{M g}{k} \)
(b) \( \frac{M g}{k}\left(1-\frac{L A \sigma}{M}\right) \)
(c) \( \frac{M g}{k}\left(1-\frac{L A \sigma}{2 M}\right) \)
(d) \( \frac{M g}{k}\left(1+\frac{L A \sigma}{M}\right) \)
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