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: <br> (Here k is spring constant)

Question

( A ) $\frac{Mg}{k}$
( B ) $\frac{Mg}{k} (1 - \frac{L A \sigma}{M})$
( C ) $\frac{Mg}{k} (1 - \frac{L A \sigma}{2M})$
( D ) $\frac{Mg}{k} (1 + \frac{L A \sigma}{M})$