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 equlibrium is:

Explanation

`F - Kx_(0)` [restoring force in spring]
`F_(B)` = buoyant force `= (mg)_("liq.displacement")`
`= (AL)/(2) sigma g`, at equilibrium `F_(net) = 0`
From free body diagram,
`K x_(0) + (AL)/(2) sigma g = mg`
`rArr K x_(0) = mg - (AL)/(2) sigma g`
`x_(0) = (mg)/(K) [1 - (AL sigma)/(2m)]`