A uniform cylinder of length

Question:

A uniform cylinder of length $\mathrm{L}$ and mass $\mathrm{M}$ having cross- sectional area A is suspended, with its length vertical, form 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 :

(Here $\mathrm{k}$ is spring constant)

  1. $\frac{\mathrm{Mg}}{\mathrm{k}}$

  2. $\frac{\mathrm{Mg}}{\mathrm{k}}\left(1-\frac{\mathrm{LA} \sigma}{\mathrm{M}}\right)$

  3. $\frac{\mathrm{Mg}}{\mathrm{k}}\left(1-\frac{\mathrm{LA} \sigma}{2 \mathrm{M}}\right)$

  4. $\frac{\mathrm{Mg}}{\mathrm{k}}\left(1+\frac{\mathrm{LA} \sigma}{\mathrm{M}}\right)$

Correct Option: , 3

Solution:

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