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

In equilibrium, upward force = downward force
`F_("spring")+F_(B)=mg rArr kx_(0)+((L)/(2)A)sigmag=mg`
`rArr x_(0)=(mg-(sigmaLAg)/(2))/(k)=(mg)/(k)(1-(sigmaLA)/(2m))`