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:

Options

A. `(Mg)/k (1-(LA sigma)/(M))`
B. `(Mg)/(k) (1-(LA sigma)/(2M))`
C. `(Mg)/(k) (1+(L A sigma)/(M))`
D. `(Mg)/(k)`

Answer

B

Explanation

At equilibrium positin of cylinder
`kx_(0)=F_(B)=Mg`
`kx_(0)+sigmaL/2Ag=Mg`
`x_(0)=(Mg-(sigmaLAg)/(2))/(k)`
`=(Mg)/(k) (1-(sigma LA)/(2M))`