$A$ 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:

• A
  $\frac{Mg}{k}$
• B
  $\frac{Mg}{k}\left( 1 - \frac{LA\sigma}{M} \right)$
• C
  $\frac{Mg}{k}\left( 1 - \frac{LA\sigma}{2M} \right)$
• D
  $\frac{Mg}{k}\left( 1 + \frac{LA\sigma}{M} \right)$