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)`
B. `(Mg)/(k)[1-(L a sigma)/(M)]`
C. `(Mg)/(l)[1-(L A sigma)/(2M)]`
D. `(Mg)/(k)[1+(L A sigma)/(M)]`

Answer

C

Explanation

At equililbrium position,
`kx_(0)+F_(B)=Mg`
or `kx_(0)=Mg - F_(B) =Mg -(AL sigma g)/(2)`
or `x_(0)=(1)/(k)[Mg-(AL sigma g)/(2)] = (Mg)/(k)[1-(sigma AL)/(2 M)]`