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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 σ at equilibrium position. The extension x 0 of the spring when it is in equilibrium is - (Here k is spring constant)

1. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ σ − M 2 LA 1 k Mg
2. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ σ + M LA 1 k Mg
3. k Mg
4. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ σ − M LA 1 k Mg

Correct answer: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ σ − M 2 LA 1 k Mg

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