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 σ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is : (Here, k is spring constant)

Question

$\begin{array}{1 1}(1) \large\frac{Mg}{k} \\(2) \frac{Mg}{k} \bigg(1- \frac{LA \sigma}{M} \bigg) \\ (3) \large\frac{Mg}{k} \bigg( 1- \large\frac{LA \sigma}{2M} \bigg) \\ (4) \large\frac{Mg}{k} \bigg(1+ \large\frac{LA \sigma}{M} \bigg)\end{array} $